Journal articles: 'Three-dimensional loading constraints'

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Fuellerer, Guenther, Karl F. Doerner, Richard F. Hartl, and Manuel Iori. "Metaheuristics for vehicle routing problems with three-dimensional loading constraints." European Journal of Operational Research 201, no. 3 (2010): 751–59. http://dx.doi.org/10.1016/j.ejor.2009.03.046.

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Bortfeldt, Andreas, and Junmin Yi. "The Split Delivery Vehicle Routing Problem with three-dimensional loading constraints." European Journal of Operational Research 282, no. 2 (2020): 545–58. http://dx.doi.org/10.1016/j.ejor.2019.09.024.

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Gzara, Fatma, Samir Elhedhli, and Burak C. Yildiz. "The Pallet Loading Problem: Three-dimensional bin packing with practical constraints." European Journal of Operational Research 287, no. 3 (2020): 1062–74. http://dx.doi.org/10.1016/j.ejor.2020.04.053.

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Junqueira, Leonardo, Reinaldo Morabito, and Denise Sato Yamashita. "Three-dimensional container loading models with cargo stability and load bearing constraints." Computers & Operations Research 39, no. 1 (2012): 74–85. http://dx.doi.org/10.1016/j.cor.2010.07.017.

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Chen, Zongyi, Mingkang Yang, Yijun Guo, Yu Liang, Yifan Ding, and Li Wang. "The Split Delivery Vehicle Routing Problem with Three-Dimensional Loading and Time Windows Constraints." Sustainability 12, no. 17 (2020): 6987. http://dx.doi.org/10.3390/su12176987.

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Besides routing and packing plans, synthetically considering the requirements of customers about service time is absolutely necessary. An order split delivery plan can not only better satisfy the service time requirements, but also improve the full-load rate of vehicles. The split delivery vehicle routing problem with three-dimensional loading constraints (3L-SDVRP) combines vehicle routing and three-dimensional loading with additional packing constraints. In the 3L-SDVRP splitting deliveries of customers is basically possible, i.e., a customer can be visited in two or more tours. The vehicle routing problem with three-dimensional loading constraints that are based on the time window and considering split delivery of orders (3L-CVRPTWSDO) and its optimization algorithm are studied in this paper. We established mathematical model of the problem and designed the tabu search algorithm. Based on the examples used in Gendreau et al. (2006), examples was constructed to test our algorithm. The experimental results have expressed that, in the 3L-CVRP problem, the results of split delivery is better than those of non-split delivery, and it is easier to satisfy the time window constraints. The algorithm in this paper generates high quality solutions, it provides a effective method to solve the 3L-CVRPTWSDO problems.

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JIN, ZHIHONG, KATSUHISA OHNO, and JIALI DU. "AN EFFICIENT APPROACH FOR THE THREE-DIMENSIONAL CONTAINER PACKING PROBLEM WITH PRACTICAL CONSTRAINTS." Asia-Pacific Journal of Operational Research 21, no. 03 (2004): 279–95. http://dx.doi.org/10.1142/s0217595904000254.

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This paper deals with the three-dimensional container packing problem (3DCPP), which is to pack a number of items orthogonally onto a rectangular container so that the utilization rate of the container space or the total value of loaded items is maximized. Besides the above objectives, some other practical constraints, such as loading stability, the rotation of items around the height axis, and the fixed loading (unloading) orders, must be considered for the real-life 3DCPP. In this paper, a sub-volume based simulated annealing meta-heuristic algorithm is proposed, which aims at generating flexible and efficient packing patterns and providing a high degree of inherent stability at the same time. Computational experiments on benchmark problems show its efficiency.

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Ruan, Qingfang, Zhengqian Zhang, Lixin Miao, and Haitao Shen. "A hybrid approach for the vehicle routing problem with three-dimensional loading constraints." Computers & Operations Research 40, no. 6 (2013): 1579–89. http://dx.doi.org/10.1016/j.cor.2011.11.013.

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Lacomme, Philippe, Hélène Toussaint, and Christophe Duhamel. "A GRASP×ELS for the vehicle routing problem with basic three-dimensional loading constraints." Engineering Applications of Artificial Intelligence 26, no. 8 (2013): 1795–810. http://dx.doi.org/10.1016/j.engappai.2013.03.012.

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Junqueira, Leonardo, José F. Oliveira, Maria Antónia Carravilla, and Reinaldo Morabito. "An optimization model for the vehicle routing problem with practical three-dimensional loading constraints." International Transactions in Operational Research 20, no. 5 (2012): 645–66. http://dx.doi.org/10.1111/j.1475-3995.2012.00872.x.

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Miao, Lixin, Qingfang Ruan, Kevin Woghiren, and Qi Ruo. "A hybrid genetic algorithm for the vehicle routing problem with three-dimensional loading constraints." RAIRO - Operations Research 46, no. 1 (2012): 63–82. http://dx.doi.org/10.1051/ro/2012008.

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Männel, Dirk, and Andreas Bortfeldt. "Solving the pickup and delivery problem with three-dimensional loading constraints and reloading ban." European Journal of Operational Research 264, no. 1 (2018): 119–37. http://dx.doi.org/10.1016/j.ejor.2017.05.034.

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Bortfeldt, Andreas. "A hybrid algorithm for the capacitated vehicle routing problem with three-dimensional loading constraints." Computers & Operations Research 39, no. 9 (2012): 2248–57. http://dx.doi.org/10.1016/j.cor.2011.11.008.

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Zhu, Xiang, and Ding-you Lei. "Bi-level hybrid local search approach for three-dimensional loading problem with balancing constraints." Journal of Central South University 25, no. 4 (2018): 903–18. http://dx.doi.org/10.1007/s11771-018-3793-9.

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Ruan, Minzhi, Chunyue Shen, Jianqiang Tang, Chao Qi, and Shuang Qiu. "A Double Traveling Salesman Problem With Three-Dimensional Loading Constraints for Bulky Item Delivery." IEEE Access 9 (2021): 13052–63. http://dx.doi.org/10.1109/access.2021.3051248.

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Cao, Fei. "Study on Container Loading Problem Based on NSGA-α Algorithm". Advanced Materials Research 753-755 (серпень 2013): 2954–58. http://dx.doi.org/10.4028/www.scientific.net/amr.753-755.2954.

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Container loading problem with multi-constraints is usually modeled as a three-dimensional packing problem which is known to be NP-complete. This paper presents a novel approach to resolve the container loading problem via multi-objective optimization algorithm (NSGA-II). Specific encoding method and genetic operators are designed based on the mathematics description of the problem. The process also takes several practical constraints into account. Simulation results show that this approach is feasible and effective.

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Chenguang, Yang, Liu Hu, and Gao Yuan. "Load Planning of Transport Aircraft Based on Hybrid Genetic Algorithm." MATEC Web of Conferences 179 (2018): 01007. http://dx.doi.org/10.1051/matecconf/201817901007.

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Loading of transport aircraft attracts much attention as the airlift is developing rapidly. It refers to the process that various cargoes are loaded, in an appropriate manner, into kinds of transport aircrafts with constraints of volume, weight and gravity center. Based on two-dimensional bin packing with genetic algorithm (GA), a new hybrid algorithm is proposed to solve the multi-constraint loading problem of transport aircraft for seeking the minimum of fuel consumption. Heuristic algorithm is applied to optimize single-aircraft loading in GA decoding, and the procedure of hybrid GA is summarized for the multi-aircraft loading issues. In the case study, eight kinds of cargos are distributed in three different aircrafts. The optimal result indicates that this algorithm can rapidly generate the best plan for the loading problem regarding lower transport costs.

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Mahvash, Batoul, Anjali Awasthi, and Satyaveer Chauhan. "A column generation based heuristic for the capacitated vehicle routing problem with three-dimensional loading constraints." International Journal of Production Research 55, no. 6 (2016): 1730–47. http://dx.doi.org/10.1080/00207543.2016.1231940.

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Koch, Henriette, Maximilian Schlögell, and Andreas Bortfeldt. "A hybrid algorithm for the vehicle routing problem with three-dimensional loading constraints and mixed backhauls." Journal of Scheduling 23, no. 1 (2019): 71–93. http://dx.doi.org/10.1007/s10951-019-00625-7.

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Mahvash, Batoul, Anjali Awasthi, and Satyaveer Chauhan. "A Column Generation Based Heuristic for the Capacitated Vehicle Routing Problem with Three-dimensional Loading Constraints." IFAC-PapersOnLine 48, no. 3 (2015): 448–53. http://dx.doi.org/10.1016/j.ifacol.2015.06.122.

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Zhang, Qun, Li Rong Wei, Rui Hu, Rui Yan, Li Hua Li, and Xiao Ning Zhu. "A Review on the Bin Packing Capacitated Vehicle Routing Problem." Advanced Materials Research 853 (December 2013): 668–73. http://dx.doi.org/10.4028/www.scientific.net/amr.853.668.

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This paper introduced the Bin Packing Capacitated Vehicle Routing Problem. It introduced the constraints and differences between algorithms of two-dimensional and three-dimensional loading capacitated vehicle routing problem. It gave a review of models and algorithms for Bin Packing Capacitated VRP. Finally, it prospected future research orientations and possible improvement in this area.

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Wei, Lijun, Zhenzhen Zhang, and Andrew Lim. "An Adaptive Variable Neighborhood Search for a Heterogeneous Fleet Vehicle Routing Problem with Three-Dimensional Loading Constraints." IEEE Computational Intelligence Magazine 9, no. 4 (2014): 18–30. http://dx.doi.org/10.1109/mci.2014.2350933.

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Männel, Dirk, and Andreas Bortfeldt. "A hybrid algorithm for the vehicle routing problem with pickup and delivery and three-dimensional loading constraints." European Journal of Operational Research 254, no. 3 (2016): 840–58. http://dx.doi.org/10.1016/j.ejor.2016.04.016.

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Koch, Henriette, Andreas Bortfeldt, and Gerhard Wäscher. "A hybrid algorithm for the vehicle routing problem with backhauls, time windows and three-dimensional loading constraints." OR Spectrum 40, no. 4 (2018): 1029–75. http://dx.doi.org/10.1007/s00291-018-0506-6.

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Ayough, Ashkan, Behrooz Khorshidvand, Negah Massomnedjad, and Alireza Motameni. "An integrated approach for three-dimensional capacitated vehicle routing problem considering time windows." Journal of Modelling in Management 15, no. 3 (2020): 995–1015. http://dx.doi.org/10.1108/jm2-11-2018-0183.

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Purpose As a critical problem in sophisticated distribution systems, vehicle routing plays a pivotal role in dealing with time windows and capacities constraints. The purpose of this paper is to addresses a new integrated model to incorporate both three-dimensional and time windows aspects of the routing problem. First, capacitated vehicle routing decisions are made subject to a soft time interval to meet the customers’ demands. Afterward, these decisions are entered into the three-dimensional loading problem. Design/methodology/approach The problem is solved using generalized algebraic modeling system software in small-size problems. The problem is NP-hard and requires an efficient solution methodology. For this purpose, a hybrid algorithm has been proposed to solve the large-size problems. The efficiency of this algorithm is checked by making comparisons with exact solutions for small and medium size test problems, and with the related literature for large size problems. Findings The numerical experiments show that the proposed model covers more effectively the broader aspects of the transportation problem. Furthermore, the proposed algorithm supports competitive and satisfactory results by giving reasonable outputs in comparison with previous studies. Originality/value The main purpose of this integration is to achieve minimum total transportation costs, which cannot be guaranteed without applying two referred constraints, simultaneously.

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Zhang, Zhenzhen, Lijun Wei, and Andrew Lim. "An evolutionary local search for the capacitated vehicle routing problem minimizing fuel consumption under three-dimensional loading constraints." Transportation Research Part B: Methodological 82 (December 2015): 20–35. http://dx.doi.org/10.1016/j.trb.2015.10.001.

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Berto, Filippo, and Alberto Campagnolo. "Three-dimensional cracked discs under anti-plane loading and effects of the boundary conditions." International Journal of Structural Integrity 6, no. 4 (2015): 541–64. http://dx.doi.org/10.1108/ijsi-02-2015-0007.

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Purpose – Accordingly to the recent multi-scale model proposed by Sih and Tang, different orders of stress singularities are related to different material dependent boundary conditions associated with the interaction between the V-notch tip and the material under the remotely applied loading conditions. This induces complex three-dimensional stress and displacement fields in the proximity of the notch tip, which are worthy of investigation. The paper aims to discuss these issues. Design/methodology/approach – Starting from Sih and Tang’s model, in the present contribution the authors propose some analytical expressions for the calculation of the strain energy density (SED) averaged over a control volume embracing the V-notch tip. The expressions vary as a function of the different boundary conditions. Dealing with the specific crack case, the results from the analytical frame are compared with those determined numerically under linear-elastic hypotheses, by applying different constraints to the through-the-thickness crack edges in three-dimensional discs subjected to Mode III loading. Free-free and free-clamped cases are considered. Findings – Due to three-dimensional effects, the application of a nominal Mode III loading condition automatically provokes coupled Modes (I and II). Not only the intensity of the induced modes but also their degree of singularity depend on the applied conditions on the crack flanks. The variability of local SED through the thickness of the disc is analysed by numerical analyses and compared with the theoretical trend. Originality/value – The capability of the SED to capture the combined three-dimensional effects is discussed in detail showing that this parameter is particularly useful when the definition of the stress intensity factors (SIFs) is ambiguous or the direct comparison between SIFs with odd dimensionalities is not possible.

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Zhou, Yuan-de, Kai Xu, Xinwei Tang, and Leslie George Tham. "Three-Dimensional Modeling of Spatial Reinforcement of Soil Nails in a Field Slope under Surcharge Loads." Journal of Applied Mathematics 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/926097.

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Soil nailing has been one of the most popular techniques for improving the stability of slopes, in which rows of nails and a structural grillage system connecting nail heads are commonly applied. In order to examine the spatial-reinforcement effect of soil nails in slopes, a three-dimensional (3D) numerical model has been developed and used to back-analyze a field test slope under surcharge loading. Incremental elastoplastic analyses have been performed to study the internal deformation within the slope and the development of nail forces during the application of top surcharge loads. Different treatments of the grillage constraints at nail heads have been studied. It is shown that the numerical predictions compare favorably with the field test measurements. Both the numerical and the field test results suggest that soil nails are capable of increasing the overall stability of a loose fill slope for the loading conditions considered in this study. The axial force mobilization in the two rows of soil nails presents a strong dependence on the relative distance with the central section. With the surcharge loads increased near the bearing capacity of the slope, a grillage system connecting all the nail heads can affect the stabilizing mechanism to a notable extent.

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AlHamaydeh, Mohammad, Samer Barakat, and Omar Nasif. "Optimization of Support Structures for Offshore Wind Turbines Using Genetic Algorithm with Domain-Trimming." Mathematical Problems in Engineering 2017 (2017): 1–14. http://dx.doi.org/10.1155/2017/5978375.

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The powerful genetic algorithm optimization technique is augmented with an innovative “domain-trimming” modification. The resulting adaptive, high-performance technique is called Genetic Algorithm with Domain-Trimming (GADT). As a proof of concept, the GADT is applied to a widely used benchmark problem. The 10-dimensional truss optimization benchmark problem has well documented global and local minima. The GADT is shown to outperform several published solutions. Subsequently, the GADT is deployed onto three-dimensional structural design optimization for offshore wind turbine supporting structures. The design problem involves complex least-weight topology as well as member size optimizations. The GADT is applied to two popular design alternatives: tripod and quadropod jackets. The two versions of the optimization problem are nonlinearly constrained where the objective function is the material weight of the supporting truss. The considered design variables are the truss members end node coordinates, as well as the cross-sectional areas of the truss members, whereas the constraints are the maximum stresses in members and the maximum displacements of the nodes. These constraints are managed via dynamically modified, nonstationary penalty functions. The structures are subject to gravity, wind, wave, and earthquake loading conditions. The results show that the GADT method is superior in finding best discovered optimal solutions.

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Bouchitté, Guy, Ornella Mattei, Graeme W. Milton, and Pierre Seppecher. "On the forces that cable webs under tension can support and how to design cable webs to channel stresses." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2223 (2019): 20180781. http://dx.doi.org/10.1098/rspa.2018.0781.

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In many applications of structural engineering, the following question arises: given a set of forces f 1 , f 2 , …, f N applied at prescribed points x 1 , x 2 , …, x N , under what constraints on the forces does there exist a truss structure (or wire web) with all elements under tension that supports these forces? Here we provide answer to such a question for any configuration of the terminal points x 1 , x 2 , …, x N in the two- and three-dimensional cases. Specifically, the existence of a web is guaranteed by a necessary and sufficient condition on the loading which corresponds to a finite dimensional linear programming problem. In two dimensions, we show that any such web can be replaced by one in which there are at most P elementary loops, where elementary means that the loop cannot be subdivided into subloops, and where P is the number of forces f 1 , f 2 , …, f N applied at points strictly within the convex hull of x 1 , x 2 , …, x N . In three dimensions, we show that, by slightly perturbing f 1 , f 2 , …, f N , there exists a uniloadable web supporting this loading. Uniloadable means it supports this loading and all positive multiples of it, but not any other loading. Uniloadable webs provide a mechanism for channelling stress in desired ways.

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Pace, Shannon, Ayad Turky, I. Moser, and Aldeida Aleti. "Distributing Fibre Boards: A Practical Application of the Heterogeneous Fleet Vehicle Routing Problem with Time Windows and Three-dimensional Loading Constraints." Procedia Computer Science 51 (2015): 2257–66. http://dx.doi.org/10.1016/j.procs.2015.05.382.

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HUGHES, PATSY M., and JEREMY M. V. RAYNER. "Addition of Artificial Loads to Long-Eared Bats Plecotus Auritus: Handicapping Flight Performance." Journal of Experimental Biology 161, no. 1 (1991): 285–98. http://dx.doi.org/10.1242/jeb.161.1.285.

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A series of experiments is described in which two brown long-eared bats Plecotus auritus Linnaeus (Chiroptera: Vespertilionidae) were flown in a 1mx1mx4.5m flight enclosure at a range of body masses (n=9 experiments for a female bat, and n = 11 for a male bat). The highest three of these masses incorporated artificial loads. Stroboscopic stereophotogrammetry was used to make three-dimensional reconstructions (n=124) of the bats' flight paths. Over the entire range of experiments, wing loading was increased by 44% for the female and 46% for the male bat. Effects arising from captivity were controlled for: experiments at certain wing loadings were repeated after a period in captivity and the response to load was found to be unaltered. Flight speed fell with total mass M or with wing loading, varying as M−0.49 in the female and M−0.42 in the male bat. Wingbeat frequency increased with total mass or wing loading, varying as M0.61 in the female and M0.44in the male bat. Hence frequency, but not speed, changed with mass in the direction predicted by aerodynamic theory. These results were used in a mathematical model to predict wingbeat amplitude, flight power and cost of transport. The model was also used to estimate the optimal flight speeds Vmr and Vmp. The model predicted that amplitude increases with load. Measurements of wingbeat amplitude did not differ significantly from the predicted values. The observed flight speed was below the predicted minimum power speed Vmp (which increases with load), and diverged further from this with progressive loading. The increase in cost of flight calculated by the model over the range of wing loadings was approximately double that which it would have been had the bats adopted the optimal approach predicted by the model. The limitations inherent in the theoretical model, and the possible constraints acting on the animals, are discussed.

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Felix, J., and G. N. Vanderplaats. "Configuration Optimization of Trusses Subject to Strength, Displacement and Frequency Constraints." Journal of Mechanisms, Transmissions, and Automation in Design 109, no. 2 (1987): 233–41. http://dx.doi.org/10.1115/1.3267443.

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Three-dimensional elastic trusses are designed for minimum weight, subject to constraints on member stresses, Euler buckling, joint displacements and system natural frequencies. Multiple static loading conditions are considered. The finite-element displacement method of analysis is used and eigenvalues are calculated using the subspace iteration technique. All gradient information is calculated analytically. The design problem is cast as a multilevel numerical optimization problem. The joint coordinates are treated as system variables. For each proposed configuration, the member sizes are updated as a suboptimization problem. This subproblem is efficiently solved using approximation concepts in the reciprocal variable space. The multilevel approach is shown to be an effective technique which conveniently takes advantage of the most efficient methods available for the member sizing problem. Examples are presented to demonstrate the method. The optimum configuration is shown to be strongly dependent on the constraints which are imposed on the design.

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Belgherras, Mohammed Elnedhir, Boualem Serier, Ali Benouis, and Lalia Hachemi. "Mechanical Behavior of Bone Cement under Dynamic Loading." Periodica Polytechnica Mechanical Engineering 61, no. 3 (2017): 204. http://dx.doi.org/10.3311/ppme.9672.

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In orthopedic surgery and particularly in total hip arthroplasty, The fixation of the implant is generally made by the surgical cement, constituted essentially by polymer (PMMA), It is necessary to know the strengths applied to the prosthetic articulation during the current activities exercised by the patient in their life, to know the distribution of the constraints in the system (bone - cement - implant).This study aims to analyze numerically using the finite element method, the effect of activities (dynamic loads) of the patient on the level and distribution of stresses generated in the components of total hip prosthesis. Five activities, the most frequently performed by the patient such as normal walking, the up and down stairs, sitting and up from chair, were selected for this study. For this purpose, a three-dimensional model of the total hip prosthesis has been developed. The results obtained from this model show that the total hip replacement components and especially the bone cement are more highly stressed during the process of climbing stairs. These excessively high loads can lead to damage of the cement and thus the loosening of the prosthesis.

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Pullan, Graham, John Denton, and Eric Curtis. "Improving the Performance of a Turbine With Low Aspect Ratio Stators by Aft-Loading." Journal of Turbomachinery 128, no. 3 (2004): 492–99. http://dx.doi.org/10.1115/1.2182000.

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Experimental data and numerical simulations are presented from a research turbine with low aspect ratio nozzle guide vanes (NGVs). The combined effects of mechanical and aerodynamic constraints on the NGV create very strong secondary flows. This paper describes three designs of NGV that have been tested in the turbine, using the same rotor row in each case. NGV 2 used three-dimensional design techniques in an attempt to improve the performance of the datum NGV 1 blade, but succeeded only in creating an intense vortex shed from the trailing edge (as previously reported) and lowering the measured stage efficiency by 1.1% points. NGV 3 was produced to avoid the “shed vortex” while adopting a highly aft-loaded surface pressure distribution to reduce the influence of the secondary flows. The stage with NGV 3 had an efficiency 0.5% points greater than that with NGV 1. Detailed comparisons between experiment and computations, including predicted entropy generation rates, are used to highlight the areas where the loss reduction has occurred and hence to quantify the effects of employing highly aft-loaded NGVs.

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Aschmann, J., and B. M. Sinnhuber. "Contribution of very short-lived substances to stratospheric bromine loading: uncertainties and constraints." Atmospheric Chemistry and Physics Discussions 12, no. 11 (2012): 30283–326. http://dx.doi.org/10.5194/acpd-12-30283-2012.

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Abstract. Very short-lived substances (VSLS) still represent a major factor of uncertainty in the quantification of stratospheric bromine loading. One of the major obstacles for short-lived source gases in contributing to the stratosphere is generally thought to be loss of inorganic bromine (Bry) in the tropical tropopause layer (TTL) due to dehydration. We use sensitivity calculations with a~three-dimensional chemistry transport model comprising a consistent parametrization of convective transport and a comprehensive chemistry scheme to investigate the associated processes. The model considers the two most important bromine VSLS, bromoform (CHBr3) and dibromomethane (CH2Br2). The organic bromine source gases as well as the resulting profile of inorganic bromine in the model are consistent with available observations. In contrast to its organic precursors, Bry is assumed to have a~significant sorption capacity regarding sedimenting liquid or frozen particles thus the fraction of intact source gases during their ascent through the TTL is a critical factor. We find that source gas injection is the dominant pathway into the stratosphere, about 50% of CHBr3 and 93% of CH2Br2 is able to overcome the cold point tropopause at approximately 17 km altitude, modulated by the interannual variability of the vertical transport efficiency. In fact, our sensitivity calculations indicate that the extent of source gas injection of CHBr3 is highly sensitive to the strength of convection and large-scale ascent; in contrast, modifying the photolysis or the destruction via OH yields a significantly smaller response. In principal, the same applies as well to CH2Br2, though it is considerably less responsive due to its longer lifetime. The next important aspect we identified is that the partitioning of available Bry from short-lived sources is clearly shifted away from HBr, according to our current state of knowledge the only member of the Bry family which is efficiently adsorbed on ice particles. This effect is caused by very efficient heterogeneous reactions on ice surfaces which reduce the HBr/Bry fraction below 15% at the tropical tropopause. Under these circumstances there is no significant loss of Bry due to dehydration in the model, VSLS contribute fully to stratospheric bromine. In addition, we conduct several sensitivity calculations to test the robustness of this result. If heterogeneous chemistry is ignored, the HBr/Bry fraction exceeds 50% and about 10% of bromine from VSLS is scavenged. Dehydration plays a minor role for Bry removal under the assumption that HOBr is efficiently adsorbed on ice as well since the heterogeneous reactions alter the partitioning equilibrium of Bry in favor of HOBr. In this case, up to 12% of bromine from VSLS is removed. Even in the extreme and unrealistic case that adsorbed species on ice particles are instantaneously removed the maximum loss of bromine does not exceed 25%. In conclusion, considering the average abundance of bromine short-lived source gases in convective updrafts of 6 parts per trillion by volume (pptv) we find a most likely contribution of VSLS to stratospheric bromine in the range of 4.5–6 pptv.

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Aschmann, J., and B. M. Sinnhuber. "Contribution of very short-lived substances to stratospheric bromine loading: uncertainties and constraints." Atmospheric Chemistry and Physics 13, no. 3 (2013): 1203–19. http://dx.doi.org/10.5194/acp-13-1203-2013.

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Abstract. Very short-lived substances (VSLS) still represent a major factor of uncertainty in the quantification of stratospheric bromine loading. One of the major obstacles for short-lived source gases in contributing to the stratosphere is generally thought to be loss of inorganic bromine (Bry) in the tropical tropopause layer (TTL) due to dehydration. We use sensitivity calculations with a three-dimensional chemistry transport model comprising a consistent parametrization of convective transport and a comprehensive chemistry scheme to investigate the associated processes. The model considers the two most important bromine VSLS, bromoform (CHBr3) and dibromomethane (CH2Br2). The organic bromine source gases as well as the resulting profile of inorganic bromine in the model are consistent with available observations. In contrast to its organic precursors, Bry is assumed to have a significant sorption capacity regarding sedimenting liquid or frozen particles thus the fraction of intact source gases during their ascent through the TTL is a critical factor. We find that source gas injection is the dominant pathway into the stratosphere, about 50% of CHBr3 and 94% of CH2Br2 is able to overcome the cold point tropopause at approximately 17 km altitude, modulated by the interannual variability of the vertical transport efficiency. In fact, our sensitivity calculations indicate that the extent of source gas injection of CHBr3 is highly sensitive to the strength of convection and large-scale ascent; in contrast, modifying the photolysis or the destruction via OH yields a significantly smaller response. In principle, the same applies as well to CH2Br2, though it is considerably less responsive due to its longer lifetime. The next important aspect we identified is that the partitioning of available Bry from short-lived sources is clearly shifted away from HBr, according to our current state of knowledge the only member of the Bry family which is efficiently adsorbed on ice particles. This effect is caused by very efficient heterogeneous reactions on ice surfaces which reduce the HBr/Bry fraction below 15% at the tropical tropopause. Under these circumstances there is no significant loss of Bry due to dehydration in the model, VSLS contribute fully to stratospheric bromine. In addition, we conduct several sensitivity calculations to test the robustness of this result. If heterogeneous chemistry is ignored, the HBr/Bry fraction exceeds 50% and about 10% of bromine from VSLS is scavenged. Dehydration plays a minor role for Bry removal under the assumption that HOBr is efficiently adsorbed on ice as well since the heterogeneous reactions alter the partitioning equilibrium of Bry in favor of HOBr. In this case, up to 12% of bromine from VSLS is removed. Even in the extreme and unrealistic case that adsorbed species on ice particles are instantaneously removed the maximum loss of bromine does not exceed 25%. Assuming 6 parts per trillion by volume (pptv) of bromine short-lived source gases in convective updrafts, a value that is supported by observational data, we find a most likely contribution of VSLS to stratospheric bromine in the range of 4.5–6 pptv.

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Adebiyi, Adeyemi A., Jasper F. Kok, Yang Wang, et al. "Dust Constraints from joint Observational-Modelling-experiMental analysis (DustCOMM): comparison with measurements and model simulations." Atmospheric Chemistry and Physics 20, no. 2 (2020): 829–63. http://dx.doi.org/10.5194/acp-20-829-2020.

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Abstract. Mineral dust is the most abundant aerosol species by mass in the atmosphere, and it impacts global climate, biogeochemistry, and human health. Understanding these varied impacts on the Earth system requires accurate knowledge of dust abundance, size, and optical properties, and how they vary in space and time. However, current global models show substantial biases against measurements of these dust properties. For instance, recent studies suggest that atmospheric dust is substantially coarser and more aspherical than accounted for in models, leading to persistent biases in modelled impacts of dust on the Earth system. Here, we facilitate more accurate constraints on dust impacts by developing a new dataset: Dust Constraints from joint Observational-Modelling-experiMental analysis (DustCOMM). This dataset combines an ensemble of global model simulations with observational and experimental constraints on dust size distribution and shape to obtain more accurate constraints on three-dimensional (3-D) atmospheric dust properties than is possible from global model simulations alone. Specifically, we present annual and seasonal climatologies of the 3-D dust size distribution, 3-D dust mass extinction efficiency at 550 nm, and two-dimensional (2-D) atmospheric dust loading. Comparisons with independent measurements taken over several locations, heights, and seasons show that DustCOMM estimates consistently outperform conventional global model simulations. In particular, DustCOMM achieves a substantial reduction in the bias relative to measured dust size distributions in the 0.5–20 µm diameter range. Furthermore, DustCOMM reproduces measurements of dust mass extinction efficiency to almost within the experimental uncertainties, whereas global models generally overestimate the mass extinction efficiency. DustCOMM thus provides more accurate constraints on 3-D dust properties, and as such can be used to improve global models or serve as an alternative to global model simulations in constraining dust impacts on the Earth system.

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LIN, HSIU-CHEN, TUNG-WU LU, and HORNG-CHAUNG HSU. "THREE-DIMENSIONAL ANALYSIS OF KINEMATIC AND KINETIC COORDINATION OF THE LOWER LIMB JOINTS DURING STAIR ASCENT AND DESCENT." Biomedical Engineering: Applications, Basis and Communications 16, no. 02 (2004): 101–8. http://dx.doi.org/10.4015/s1016237204000153.

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Being a common daily activity, stair locomotion places much higher loads on the lower limb than level walking does so a better understanding of the biomechanics of this activity is important for evaluation and treatment for patients with lower limb problems. The purpose of the present study was to investigate the three-dimensional dynamics and coordination of the joints of the lower limb during the stance phase of stair ascent and descent. Ten normal young adult subjects were recruited to ascend and descend stairs in a gait laboratory where the three-dimensional kinematic and kinetic data as well as muscle electromyography (EMG) were collected. The sagittal ranges of motion during stance phase of stair ascent were from 1.85° extension to 53.5° flexion for the hip, 13.1° to 60.1° flexion for the knee and 13.8° dorsiflexion to 14.0° plantarflexion for the ankle. Corresponding data for stair descent were 4.78( to 13.16( flexion for the hip, 8.3° to 77.6° flexion for the knee and 18.3° dorsiflexion to 27.4° plantarflexion for the ankle. Maximum extensor moments of 8.5% and 15.6% (Nm/BW/LL) were required at the hip and knee respectively during loading response while 19.4% (Nm/BW/LL) at the ankle shortly before toe-off. During stair descent, maximum extensor moments of about 4.4% were required at the hip during loading response and before toe-off while 13.3% and 15.2% (Nm/BW/LL) at the knee and ankle respectively before toe-off The joint angles, moments, and powers in the frontal and transverse planes were relatively small, except for hip abduction. The hip abductor moments and powers were significantly bigger than those of the knee and ankle in both stair activities. Joint powers and the corresponding muscle activation patterns in stair ascent were significantly different from those in descent, with concentric powers generated mostly during stair ascent and with eccentric powers stair descent. The differences of the movements of the lower limb during stair ascent and descent were due to different safety requirements and kinematic and kinetic constraints from the stairs. The complete description of the biomechanics of the lower extremity while performing stair locomotion will be helpful for the planning and evaluation of treatment programs for patients with lower limb problems.

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Deng, Qing-Hua, Shuai Shao, Lei Fu, Hai-Feng Luan, and Zhen-Ping Feng. "An Integrated Design and Optimization Approach for Radial Inflow Turbines—Part I: Automated Preliminary Design." Applied Sciences 8, no. 11 (2018): 2038. http://dx.doi.org/10.3390/app8112038.

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An integrated design and optimization approach was developed for radial inflow turbines, which consists of two modules, an automated preliminary design module, and a flexible three-dimensional multidisciplinary optimization module. In this paper, the first module about the automated preliminary design approach was presented in detail and validated by the experimental data. The approach employs a genetic algorithm to explore the design space defined by the loading coefficient, flow coefficient, and rotational speed. The aim is to obtain the best design scheme with high aerodynamic performance under specified constraints and to reduce the dependency on human experiences when designing a radial inflow turbine. The validation results show that the present approach is able to get the optimal design and alleviate the dependence on the designer’s expertise under specified constraints at the preliminary design stage. Furthermore, the optimization results indicate that using the present optimization approach the total-to-static efficiency of the optimized T-100 radial inflow turbine can be increased by 1.0% under design condition and the rotor weight can be decreased by 0.35 kg (26.7%) as compared with that of the original case.

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Zakian, Pooya, Behnam Ordoubadi, and Erfan Alavi. "Optimal design of steel pipe rack structures using PSO, GWO, and IGWO algorithms." Advances in Structural Engineering 24, no. 11 (2021): 2529–41. http://dx.doi.org/10.1177/13694332211004116.

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Design optimization of industrial structures is of great importance for engineers in order to provide a cost-effective structural design. Meanwhile, pipe rack is a skeletal industrial structure subjected to various types of loading such as gravity, seismic, piping, and thermal forces. While there are many studies on design optimization of the most common structures, only a limited number of studies exist on optimal design of industrial structures. In this article, a design optimization problem is proposed for weight minimization of steel pipe rack structures, and then the problem is solved through three meta-heuristic algorithms consisting of a modified particle swarm optimization (PSO), grey wolf optimizer (GWO), and the recently developed improved grey wolf optimizer (IGWO). The optimization problem is in discrete form in order to consider practically available cross-sections for the structural members. Stress ratio, drift, and dimensional constraints are imposed during the optimization. In order to demonstrate the capability and effectiveness of the present design optimization problem, a pipe rack structure is optimized by the proposed algorithms, and the optimized designs are compared to an ordinary design in terms of the structural weight and the status of constraints.

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Zhang, Longxin, and Songtao Wang. "A combination application of tandem blade and endwall boundary layer suction in a highly loaded aspirated compressor outlet vane." Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 232, no. 2 (2017): 129–43. http://dx.doi.org/10.1177/0957650917722455.

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Aspirated compressor is a promising design concept to enhance the power density of the compression system; however, with regard to the rear stages of multistage aspirated compressor, the blade is fairly thin. Limited by the mechanical constraints, it seems impractical to implement the boundary layer suction on the blade suction surface. So the question arising is can we replace the blade suction surface with other feasible flow control methods without implementing extra device on the blade? To address this issue, a compound flow control method, composed of the endwall boundary layer suction and tandem blade, is proposed. The design philosophy is to utilize the EBLS to suppress the three-dimensional corner stall while to use the tandem blade to control the two-dimensional airfoil flow separation. The endwall boundary layer suction is barely implemented in the forward blade, whereas the corner flow in the rear blade is restrained by the flow through the gap between the forward and rear blades. The preliminary implement strategy of the compound flow control was presented and then applied in the design of a highly loaded aspirated compressor outlet vane. Three-dimensional numerical simulations were carried out to validate its effectiveness with different inlet boundary layer distributions. Both flow fields in the outlet vane and its loss characteristics were analyzed. The results show that, by applying the compound flow control, the outlet vane could not only achieve an aggressive loading without incurring large-scale separation at the design point but also have a considerable available incidence range. Due to the implement of the endwall boundary layer suction, the tandem blade can bring out its full potential in the two-dimensional flow control. Moreover, owing to the flow through the gap of the forward and rear blades, the aspiration flow rate required for the suppression of the three-dimensional corner stall can be reduced.

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Maffiodo, Daniela, Raffaella Sesana, Dino Paolucci, and Sabrina Bertaggia. "Finite life fatigue design of spiral springs of dual-mass flywheels: Analytical estimation and experimental results." Advances in Mechanical Engineering 10, no. 6 (2018): 168781401877847. http://dx.doi.org/10.1177/1687814018778474.

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A procedure to design the spiral springs finite life for dual-mass flywheels is presented. Due to design constraints, installation space, production processes, stiffness requirement, maximum torque, and maximum speed, these components are dimensioned for finite life. Two- and three-dimensional finite element model static structural analysis was performed to obtain the stress distribution, deformed shape, and to validate optimization design. The fatigue analysis was performed both experimentally and by means of a component life estimation model. An experimental duty cycle was applied. Finite element analysis and experimental analysis agree in pointing out the location and the value of maximum stresses and the shape of deformation. Vehicle tests highlight premature spiral springs’ failures, which do not agree with life estimation. The examination of the fracture showed that fretting and wear, along with fatigue phenomena, are the causes of premature failures. A dedicated component life estimation model is required, taking into account of wear and loading history.

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Selvaggi, I., M. Dellapasqua, F. Franci, A. Spangher, D. Visintini, and G. Bitelli. "3D COMPARISON TOWARDS A COMPREHENSIVE ANALYSIS OF A BUILDING IN CULTURAL HERITAGE." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-2 (May 30, 2018): 1061–66. http://dx.doi.org/10.5194/isprs-archives-xlii-2-1061-2018.

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Terrestrial remote sensing techniques, including both Terrestrial Laser Scanning (TLS) and Close-Range Photogrammetry (CRP), have been recently used in multiple applications and projects with particular reference to the documentation/inspection of a wide variety of Cultural Heritage structures.<br> The high density of TLS point cloud data allows to perform structure survey in an unprecedented level of detail, providing a direct solution for the digital three-dimensional modelling, the site restoration and the analysis of the structural conditions. Textural information provided by CRP can be used for the photorealistic representation of the surveyed structure. With respect to many studies, the combination of TLS and CRP techniques produces the best results for Cultural Heritage documentation purposes. Moreover, TLS and CRP point cloud data have been proved to be useful in the field of deformation analysis and structural health monitoring. They can be the input data for the Finite Element Method (FEM), providing some prior knowledge concerning the material and the boundary conditions such as constraints and loading.<br> The paper investigates the capabilities and advantages of TLS and CRP data integration for the three-dimensional modelling compared to a simplified geometric reconstruction. This work presents some results concerning the Baptistery of Aquileia in Italy, characterized by an octagonal plan and walls composed by masonry stones with good texture.

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Visentin, Peter, and Gongbing Shan. "The Kinetic Characteristics of the Bow Arm During Violin Performance: An Examination of Internal Loads as a Function of Tempo." Medical Problems of Performing Artists 18, no. 3 (2003): 91–97. http://dx.doi.org/10.21091/mppa.2003.3017.

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Studies show that 43% to 66% of professional musicians need to stop performing for extended periods due to occupational injuries, often identified as overuse syndrome. Repetitive movement may be the mechanism of these injuries, but the identification of causal factors requires quantitative research into the kinematic and kinetic characteristics of musical performance. The current study examines internal loads of the bow arm during a legato (smooth) bowing technique at a variety of tempos (speeds). Eight professional-level violinists participated in the study. A nine-camera VICON v8i system was used to capture and synchronize upper body kinematics with sound and video. Using a 10-segment biomechanical model (head, trunk, upper arms, lower arms, hands, bow, and violin) and applying inverse dynamic analysis to the kinematic data, moments and forces loading the joints (shoulder, elbow, and wrist) were calculated, revealing quantitative characteristics of the joint load. The results show that load can be measured in terms of quantity and quality, with quantity influenced by factors such as the string played and tempo and quality defined in terms of the type of load (static, quasi-static, dynamic, fundamental, and impact) and psychological and physical constraints. Inverse dynamic analysis reveals that: 1) right shoulder loads vary in quantity and quality depending on the string played, whereas wrist and elbow loads are independent of the string played; 2) loading may be divided into three discrete phases--increasing physical effort, optimization, and approaching physiologic limits; and 3) several factors contribute to impact loading, and tempo plays a dominant role. This is the first study providing quantitative three-dimensional kinematic and kinetic information on the bow and on the bow arm, laying the foundation for further exploration of the causal factors of overuse syndrome and for the potential development of practices that might minimize these injuries.

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Liacouras, Peter C., and Jennifer S. Wayne. "Computational Modeling to Predict Mechanical Function of Joints: Application to the Lower Leg With Simulation of Two Cadaver Studies." Journal of Biomechanical Engineering 129, no. 6 (2007): 811–17. http://dx.doi.org/10.1115/1.2800763.

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Computational models of musculoskeletal joints and limbs can provide useful information about joint mechanics. Validated models can be used as predictive devices for understanding joint function and serve as clinical tools for predicting the outcome of surgical procedures. A new computational modeling approach was developed for simulating joint kinematics that are dictated by bone/joint anatomy, ligamentous constraints, and applied loading. Three-dimensional computational models of the lower leg were created to illustrate the application of this new approach. Model development began with generating three-dimensional surfaces of each bone from CT images and then importing into the three-dimensional solid modeling software SOLIDWORKS and motion simulation package COSMOSMOTION. Through SOLIDWORKS and COSMOSMOTION, each bone surface file was filled to create a solid object and positioned necessary components added, and simulations executed. Three-dimensional contacts were added to inhibit intersection of the bones during motion. Ligaments were represented as linear springs. Model predictions were then validated by comparison to two different cadaver studies, syndesmotic injury and repair and ankle inversion following ligament transection. The syndesmotic injury model was able to predict tibial rotation, fibular rotation, and anterior/posterior displacement. In the inversion simulation, calcaneofibular ligament extension and angles of inversion compared well. Some experimental data proved harder to simulate accurately, due to certain software limitations and lack of complete experimental data. Other parameters that could not be easily obtained experimentally can be predicted and analyzed by the computational simulations. In the syndesmotic injury study, the force generated in the tibionavicular and calcaneofibular ligaments reduced with the insertion of the staple, indicating how this repair technique changes joint function. After transection of the calcaneofibular ligament in the inversion stability study, a major increase in force was seen in several of the ligaments on the lateral aspect of the foot and ankle, indicating the recruitment of other structures to permit function after injury. Overall, the computational models were able to predict joint kinematics of the lower leg with particular focus on the ankle complex. This same approach can be taken to create models of other limb segments such as the elbow and wrist. Additional parameters can be calculated in the models that are not easily obtained experimentally such as ligament forces, force transmission across joints, and three-dimensional movement of all bones. Muscle activation can be incorporated in the model through the action of applied forces within the software for future studies.

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Haut Donahue, Tammy L., M. L. Hull, Mark M. Rashid, and Christopher R. Jacobs. "A Finite Element Model of the Human Knee Joint for the Study of Tibio-Femoral Contact." Journal of Biomechanical Engineering 124, no. 3 (2002): 273–80. http://dx.doi.org/10.1115/1.1470171.

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As a step towards developing a finite element model of the knee that can be used to study how the variables associated with a meniscal replacement affect tibio-femoral contact, the goals of this study were 1) to develop a geometrically accurate three-dimensional solid model of the knee joint with special attention given to the menisci and articular cartilage, 2) to determine to what extent bony deformations affect contact behavior, and 3) to determine whether constraining rotations other than flexion/extension affects the contact behavior of the joint during compressive loading. The model included both the cortical and trabecular bone of the femur and tibia, articular cartilage of the femoral condyles and tibial plateau, both the medial and lateral menisci with their horn attachments, the transverse ligament, the anterior cruciate ligament, and the medial collateral ligament. The solid models for the menisci and articular cartilage were created from surface scans provided by a noncontacting, laser-based, three-dimensional coordinate digitizing system with an root mean squared error (RMSE) of less than 8 microns. Solid models of both the tibia and femur were created from CT images, except for the most proximal surface of the tibia and most distal surface of the femur which were created with the three-dimensional coordinate digitizing system. The constitutive relation of the menisci treated the tissue as transversely isotropic and linearly elastic. Under the application of an 800 N compressive load at 0 degrees of flexion, six contact variables in each compartment (i.e., medial and lateral) were computed including maximum pressure, mean pressure, contact area, total contact force, and coordinates of the center of pressure. Convergence of the finite element solution was studied using three mesh sizes ranging from an average element size of 5 mm by 5 mm to 1 mm by 1 mm. The solution was considered converged for an average element size of 2 mm by 2 mm. Using this mesh size, finite element solutions for rigid versus deformable bones indicated that none of the contact variables changed by more than 2% when the femur and tibia were treated as rigid. However, differences in contact variables as large as 19% occurred when rotations other than flexion/extension were constrained. The largest difference was in the maximum pressure. Among the principal conclusions of the study are that accurate finite element solutions of tibio-femoral contact behavior can be obtained by treating the bones as rigid. However, unrealistic constraints on rotations other than flexion/extension can result in relatively large errors in contact variables.

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Liu, Han Wu, Gui Bing Pu, Yun Hui Du, and Peng Zhang. "Finite Element Analysis of Static Strength and Fatigue Strength of Hydraulic Shield Support." Advanced Materials Research 332-334 (September 2011): 2161–65. http://dx.doi.org/10.4028/www.scientific.net/amr.332-334.2161.

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By using the geometry modeling software Pro/E, the three-dimensional model of hydraulic shield support has been built. Considering of the loading conditions and displacement constraints which the hydraulic shield support suffers from under the actual working conditions, the static strength and fatigue strength of the hydraulic shield support were analyzed by FEM when they were in two different typical working conditions of the support height, and the weakest part which was discovered in the analysis was improved in its structure. The study results showed that the designed hydraulic shield support could meet the requests of the static strength and fatigue strength. The column of the hydraulic shield support and the ear plate which locates in the connection area of the column and the push beam are the weakest parts. The counterforce given by the ground mainly focuses on the mid-back position of the hydraulic shield support, which meets the requirements of saving labor when they were removed. In the Finite Element Analysis when the reinforcement ribs were added to the ear plate, we found that the maximum equivalent stress is reduced by 150 MPa and the fatigue life coefficient is reduced markedly as well. The possibility of the fatigue breakage was decreased largely after the structure was modified and the service life of the hydraulic shield support was improved. These prove that the improvement of the hydraulic shield support structure is reasonable and feasible.

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Zhang, Tao, Ningyuan Guo, Xiaoxia Sun, et al. "A Systematic Framework for State of Charge, State of Health and State of Power Co-Estimation of Lithium-Ion Battery in Electric Vehicles." Sustainability 13, no. 9 (2021): 5166. http://dx.doi.org/10.3390/su13095166.

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Due to its advantages of high voltage level, high specific energy, low self-discharging rate and relatively longer cycling life, the lithium-ion battery has been widely used in electric vehicles. To ensure safety and reduce degradation during the lithium-ion battery’s service life, precise estimation of its states like state of charge (SOC), capacity and peak power is indispensable. This paper proposes a systematic co-estimation framework for the lithium-ion battery in electric vehicle applications. First, a linearized equivalent circuit-based battery model, together with an affine projection algorithm is used to estimate the model parameters. Then the state of health (SOH) estimator is triggered weekly or semi-monthly offline to update capacity based on the three-dimensional response surface open circuit voltage model and particle swarm optimization algorithm for accurate online SOC and state of power (SOP) estimation. At last, the Unscented Kalman Filter utilizes the estimated model parameters and updated capacity to estimate SOC online and the SOP estimator provides the power limitations considering SOC, current and voltage constraints, taking advantage of the information from both SOH and SOC estimators. Experiments show that the relative error of the SOH estimator is under 1% in all aging states whatever the loading profile is. The mean absolute SOC estimation error is under 1.6% even when the battery undergoes 744 aging cycles. The SOP estimator is validated by means of the calibrated battery model based on the HPPC test and its performance is ideal.

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Goel, V. K., J. M. Winterbottom, J. N. Weinstein, and Y. E. Kim. "Load Sharing Among Spinal Elements of a Motion Segment in Extension and Lateral Bending." Journal of Biomechanical Engineering 109, no. 4 (1987): 291–97. http://dx.doi.org/10.1115/1.3138683.

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A linear optimization model was formulated using a semi-experimental protocol to estimate the forces in the spinal elements of a lumbar motion segment subjected to an extension or lateral bending moment with and without a 120 N compressive preload. A morphometer was used to acquire the three-dimensional locations of the disk center, facet centers and ligament origin and insertion sites with the specimen in a “neutral” position. The relative motion of the superior vertebra, under the loading conditions tested, was monitored using a Selspot II® system. These data allowed the formulation of the static equilibrium equations for the superior vertebra at each of the loading conditions mentioned above. A linear optimization technique was used, along with a suitable cost function, to find an optimum solution for the set of equations and imposed constraints. Results showed that for 6.9 Nm of extension moment, each facet carried a load of 52 N, with the disk carrying an axial tensile load of 104 N. At the 6.9 Nm extension moment coupled with 120 N preload, each facet carried a load of 77.2 N and the disk an axial tensile load of 37 N. In right lateral bending, with and without preload, the load was distributed among the right facet, the disk, the left ligamentum flavum and the left capsular ligament. At the 6.9 Nm load step without preload the right facet carried an axial load of 127.01 N with the disk carrying an axial compressive load of 7.8 N. Ligament forces for this step for the left ligamentum flavum and capsular ligament, respectively, were 61.03 N and 65.14 N. The addition of 120 N of preload reduced the load on the right facet to 83.5 N. The compressive load in the disk increased to 107.5 N. The corresponding ligament forces were 43.2 N (left ligamentum flavum) and 50.7 N (left capsular ligament).

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Yusof, Feizal, and Karh Heng Leong. "Elastic-plastic J-Tz dominance in bending and tension loadings." International Journal of Structural Integrity 10, no. 5 (2019): 644–59. http://dx.doi.org/10.1108/ijsi-04-2019-0031.

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Purpose Crack tip stresses are used to relate the ability of structures to perform under the influence of cracks and defects. One of the methods to determine three-dimensional crack tip stresses is through the J-Tz method. The J-Tz method has been used extensively to characterize the stresses of cracked geometries that demonstrate positive T-stress but limited in characterizing negative T-stresses. The purpose of this paper is to apply the J-Tz method to characterize a three-dimensional crack tip stress field in a changing crack length from positive to negative T-stress geometries. Design/methodology/approach Elastic-plastic crack border fields of deep and shallow cracks in tension and bending loads were investigated through a series of three-dimensional finite element (FE) and analytical J-Tz solutions for a range of crack lengths ranging from 0.1⩽a/W⩽0.5 for two thickness extremes of B/(W − a)=1 and 0.05. Findings Both the FE and the J-Tz approaches showed that the combined in-plane and the out-of-plane constraint loss were differently affected by the T-stress and the out-of-plane size effects when the crack length changed from deep to shallow cracks. The conditions of the J-Tz dominance on the three-dimensional crack front tip were shown to be limited to positive T-stress geometries, and the J-Tz-Q2D approach can extend the crack border dominance of the three-dimensional deep and shallow bend models along the crack front tip until perturbed by an elastic-plastic corner field. Practical implications The paper reports the limitation of the J-Tz approach, which is used to calculate the state of three-dimensional crack tip stresses in power law hardening materials. The results from this paper suggest that the characterization of the three-dimensional crack tip stress in power law hardening materials is still an open issue and requires other suitable solutions to solve the problem. Originality/value This paper demonstrates a thorough analysis of a three-dimensional elastic-plastic crack tip fields for geometries that are initially either fully constrained (positive T-stress) or unconstrained (negative T-stress) crack tip fields but, subsequently, the T-stress sign changes due to crack length reduction and specimen thickness increase. The J-Tz stress-based method has been tested and its dominance over the crack tip field is shown to be affected by the combined in-plane and the out-of-plane constraints and the corner field effects.

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Journal articles on the topic 'Three-dimensional loading constraints'

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