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Journal articles on the topic 'Principle of minimum potential energy'

Author: Grafiati

Published: 4 June 2021

Last updated: 17 February 2022

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1

Chen, Xu, Pingjia Xiong, and Jianghong Ma. "Minimum Potential Energy Principle on Slip Calculation of Composite Beams." IOP Conference Series: Earth and Environmental Science 304 (September 18, 2019): 032040. http://dx.doi.org/10.1088/1755-1315/304/3/032040.

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2

Russo, Remigio. "On the principle of minimum potential energy in asymmetric elastostatics." International Journal of Engineering Science 23, no. 6 (January 1985): 659–63. http://dx.doi.org/10.1016/0020-7225(85)90135-1.

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3

Fu, Bao Lian, and Ying Jie Chen. "Springback Variation Principles in Materials Forming Processes." Applied Mechanics and Materials 29-32 (August 2010): 525–30. http://dx.doi.org/10.4028/www.scientific.net/amm.29-32.525.

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The conceptions of springback anti-couple systems and equations are initially given. By the use of the weighted residual method to the springback anti-couple equations, the springback principles of minimum potential energy and minimum complementary energy are established. Meanwhile, the springback principle of minimum potential energy is applied to calculating springback deformations of a curved beam under the radial and circumferential forces and end bending moments.

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4

SONG, Liming, Zhi ZHANG, Junting YUAN, and Yuwei LI. "Numeric modeling of a pelagic longline based on minimum potential energy principle." Journal of Fishery Sciences of China 18, no. 5 (September 3, 2013): 1170–78. http://dx.doi.org/10.3724/sp.j.1118.2011.01170.

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5

Sabaryati, J., L. S. Utami, A. W. Hasanah, and S. Viridi. "Viewing buoyant force as an application of principle of minimum potential energy." Journal of Physics: Conference Series 1816, no. 1 (February 1, 2021): 012110. http://dx.doi.org/10.1088/1742-6596/1816/1/012110.

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6

Liwen, Guan, Xu Huayang, and Liu Zhihua. "Kinematic analysis of cable-driven parallel mechanisms based on minimum potential energy principle." Advances in Mechanical Engineering 7, no. 12 (December 2015): 168781401562233. http://dx.doi.org/10.1177/1687814015622339.

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7

Guang-zu, Chen. "Determining the stress intensity factor by using the principle of minimum potential energy." Applied Mathematics and Mechanics 8, no. 12 (December 1987): 1191–99. http://dx.doi.org/10.1007/bf02450913.

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8

Gao, David Yang. "Dual Extremum Principles in Finite Deformation Theory With Applications to Post-Buckling Analysis of Extended Nonlinear Beam Model." Applied Mechanics Reviews 50, no. 11S (November 1, 1997): S64—S71. http://dx.doi.org/10.1115/1.3101852.

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The critical points of the generalized complementary energy variation principles are clarified. An open problem left by Hellinger and Reissner is solved completely. A pure complementary energy (involving the Kirchhoff type stress only) is constructed, and a complete duality theory in geometric nonlinear system is established. We prove that the well-known generalized Hellenger-Reissner’s energy L(u,s) is a saddle point functional if and only if the Gao-Strang gap function is positive. In this case, the system is stable and the minimum potential energy principle is equivalent to a unique maximum dual variational principle. However, if this gap function is negative, then L(u,s) is a so-called ∂+-critical point functional. In this case, the system has two extremum complementary principles. An interesting trinity theorem for nonconvex variational problem is discovered, which can be used to study nonlinear bifurcation problems, phase transitions, variational inequality, and other things. In order to study the shear effects in frictional post-buckling problems, a new second order 2-D nonlinear beam model is developed. Its total potential is a double-well energy. A stability criterion for post-buckling analysis is proposed, which shows that the minimax complementary principle controls a stable buckling state. The unilaterial buckling state is controled by a minimum complementary principle. However, the maximum complementary principle controls the phase transitions.

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9

Fan, Xiao Chun, Hu Chen, Yue Liu, and Wei Cang Lv. "Lifting Point Optimization of Large Steel Truss on the Principle of Minimum Potential Energy." Advanced Materials Research 919-921 (April 2014): 158–63. http://dx.doi.org/10.4028/www.scientific.net/amr.919-921.158.

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The integral hoisting construction technology of large steel truss has been widely used in the steel structure construction. Based on the principle of strain energy, the feasibility analysis on lifting point optimization of Wuhan public house’s large steel truss was conducted. It expounded the integral lifting construction technology of Wuhan public house’s large steel truss. Through the 12 different methods of lifting point setting and the application of finite element analysis software SAP2000, it discussed the optimization method of hoisting points of large steel truss on the principle of minimum potential energy. It achieved the change rule of the whole strain energy of steel truss. The scheme of 10 lifting points was identified on the economy and construction conditions. The stress state, the structural deformation state and the steady mode was analyzed under the optimum lifting point condition. The results meet the design and construction requirements, and this research method can provide the certain reference value for similar engineering.

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10

Niedziela, Julia. "Lokalizacja instalacji odnawialnych źródeł energii – aspekty prawne." Studia Iuridica, no. 86 (June 14, 2021): 196–211. http://dx.doi.org/10.31338/2544-3135.si.2020-86.13.

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The article analyses in detail legal regulations governing the location of wind and photovoltaic farms. It also describes the basic planning instruments adopted in Poland. The analysis includes the principles adopted in the so-called “Distance Law”, i.e. the principle of investment location based on the local spatial development plan, and the principle of minimum distance of a wind tourbine from residential buildings. Next, the decisions permitting the location of PV farm were described - the decision on development conditions and the decision on the location of a public purpose investment. The article identifies legal and factual problems related to the adoption of legal regulations and offers potential solutions.

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11

Fei, Xiang, Yong Lai Zheng, Wei Wei Yang, and Shu Xin Deng. "Pile Groups Displacement Calculation Based on Mindlin Solution and Principle of Minimum Potential Energy." Applied Mechanics and Materials 525 (February 2014): 541–45. http://dx.doi.org/10.4028/www.scientific.net/amm.525.541.

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A displacement function of a single pile among pile groups was proposed according to Mindlin solution. Using variational theory and principle of minimum potential energy and considering the relation between shear stress of soil around piles and displacement described in Randolph single pile displacement solution, the relation between soil and settlement in the tip of a pile was derived. Relation between load and displacement of a single pile among pile groups was obtained. It was compared with other examples after that. The result calculated by the method proposed here matchs closely with the result calculated by other methods.

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12

Pavlou, Dimitrios G. "Fatigue Crack Deflection-Induced Retardation Based on the Principle of the Minimum Potential Energy." International Review of Mechanical Engineering (IREME) 9, no. 3 (May 31, 2015): 324. http://dx.doi.org/10.15866/ireme.v9i3.6153.

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13

Temür, Rasim, Gebrail Bekdaş, and Yusuf Cengiz Toklu. "Total potential energy minimization method in structural analysis considering material nonlinearity." Challenge Journal of Structural Mechanics 3, no. 3 (September 18, 2017): 129. http://dx.doi.org/10.20528/cjsmec.2017.02.005.

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Minimum potential energy principle is the basis of the most of the well-known traditional techniques used in the structural analysis. This principle determines the equilibrium conditions of systems with reference to minimization of the sum of the total potential energy of the structure. In traditional applications, this methodology is formulized by using matrix operations. A methodology has been proposed in the last decades for structural analyses based on the idea of using metaheuristic algorithms to obtain minimum potential energy of the structural system instead of following this classical approach. This new method, called “Total Potential Optimization using Metaheuristic Algorithms (TPO/MA)”, has been applied in this paper to truss structures considering linear and nonlinear behavior of the structural material. The metaheuristic method used in this process is teaching-learning based optimization (TLBO) algorithm. The proposed technique is applied on numerical examples and results are compared with other techniques in order to test the efficiency of the proposed method. According to results obtained, TPO/MA method with TLBO algorithm is a feasible technique for the investigated problem.

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14

Zhong, Xiang Qiang, Li Dong Liang, and Yan Hong Yang. "Research on Ship Part Nesting System Based on Energy Principle and Intelligent Optimization." Advanced Materials Research 694-697 (May 2013): 2771–74. http://dx.doi.org/10.4028/www.scientific.net/amr.694-697.2771.

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A nesting system based on minimum potential energy principle and intelligent optimization for ship part nesting problem was proposed. Discussing polygon judgment and separation, intersection test and collision problems of ship parts, a kind of polygon overlap detection method was put forward, and contacting process was analyzed by use of envelope rectangle intersection test algorithm; During analyzing ship part nesting process based on minimum potential energy principle and genetic algorithm fusion, basic physical meaning of nesting problem was explained from mechanics. Throng intelligent ship part nesting system verification, the algorithm is feasible, physical meaning is clear; it can realize ship part nesting.

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15

Campanile, Antonio. "Floating Body Equilibrium by Potential-Energy Minimization." Marine Technology and SNAME News 28, no. 03 (May 1, 1991): 153–62. http://dx.doi.org/10.5957/mt1.1991.28.3.153.

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The paper presents a computer-based approach aiming to solve the equilibrium equations of a floating body by means of potential-energy minimization. After a brief and general discussion, the principle that the potential energy of the system must be at a minimum is adopted as the condition for identifying the stable equilibrium positions of a marine vehicle. A consistent mathematical formulation is then developed. The problem is solved, therefore, by searching for the minimum of a function of three variables using a simple and efficient iterative method. This makes it possible for the equilibrium positions to be determined directly, unlike the classic methods-that is, without any previously constructed table of hydrostatic data and regardless of the magnitude of waterplane rotation compared with the initial orientation. No restriction is stipulated on hull form. Some study cases relating to a prismatic barge and a jacket-type platform are presented and analyzed. Relevant numerical results allow the procedure to be optimized so as to improve convergence. Finally, peculiar features of the proposed method are discussed, with particular reference to jacket-type offshore platforms, and further valuable applications are indicated.

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16

Ou, Qiang, Ling Zhang, Minghua Zhao, and Yixian Wang. "Lateral Displacement and Internal Force in Diaphragm Walls Based on Principle of Minimum Potential Energy." International Journal of Geomechanics 19, no. 6 (June 2019): 04019055. http://dx.doi.org/10.1061/(asce)gm.1943-5622.0001415.

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17

Marichev, Victor A. "Surface energy and surface tension of condensed matter and the principle of minimum potential energy of systems (revised)." Journal of Solid State Electrochemistry 16, no. 12 (August 10, 2012): 3675–81. http://dx.doi.org/10.1007/s10008-012-1832-2.

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18

Maceda, Marco, and Jairo Villafuerte-Lara. "Perturbative calculation of energy levels for the Dirac equation with generalized momenta." International Journal of Modern Physics A 35, no. 20 (July 15, 2020): 2050106. http://dx.doi.org/10.1142/s0217751x20501067.

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We analyze a modified Dirac equation based on a noncommutative structure in phase space originating from a generalized uncertainty principle with a minimum length. The noncommutative structure induces generalized momenta and contributions to the energy levels of the standard Dirac equation. Applying techniques of perturbation theory, we find the lowest-order corrections to the energy levels and eigenfunctions of the Dirac equation in three dimensions for a spherically symmetric linear potential and for a square-well times triangular potential along one spatial dimension. We find that the corrections due to the noncommutative contributions may be of the same order as the relativistic ones, leading to an upper bound on the parameter fixing the minimum length induced by the generalized uncertainty principle.

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19

Taylor, J. E. "A Global Extremum Principle in Mixed Form for Equilibrium Analysis With Elastic/Stiffening Materials (a Generalized Minimum Potential Energy Principle)." Journal of Applied Mechanics 61, no. 4 (December 1, 1994): 914–18. http://dx.doi.org/10.1115/1.2901577.

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An extremum problem formulation is presented for the equilibrium mechanics of continuum systems made of a generalized form of elastic/stiffening material. Properties of the material are represented via a series composition of elastic/locking constituents. This construction provides a means to incorporate a general model for nonlinear composites of stiffening type into a convex problem statement for the global equilibrium analysis. The problem statement is expressed in mixed “stress and deformation” form. Narrower statements such as the classical minimum potential energy principle, and the earlier (Prager) model for elastic/locking material are imbedded within the general formulation. An extremum problem formulation in mixed form for linearly elastic structures is available as a special case as well.

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20

Wen, Shu Jie, You Li, and Xin Chen. "Stability Analysis of Slope with Arbitrary Sliding Surface on Multi Strata Using Minimum Potential Energy Principle." Advanced Materials Research 250-253 (May 2011): 2588–91. http://dx.doi.org/10.4028/www.scientific.net/amr.250-253.2588.

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As a rule,the natural slope is not homogeneous,and its sliding surface is arbitrary. However,the common slope stability analysis methods used to assume shape of sliding surface and slope homogeneity,and the calculation process is so complex that accuracy of results is decreasing.In this study,the potential energy function of sliding body is established for slope with arbitrary sliding surface on multi strata.Using minimum potential energy principle, the displacement of sliding body can be got. Then based on Moore - Coulomb criterion and condition of force equilibrium in the sliding direction, the safety factor can be got directly. Case studies show: ①This slope stability analysis methods is valid.② Different definition of safety factor leads to different analysis result.

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21

Liang, Bin, Fan Shen Meng, and Rui Mao. "Study on Interface Slips in Concrete Filled Square Steel Tubular Column." Advanced Materials Research 163-167 (December 2010): 888–92. http://dx.doi.org/10.4028/www.scientific.net/amr.163-167.888.

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Based on the principle of minimum potential energy, the interface slips in concrete filled square steel tubular column is calculated. According to the study of bond-slip behaviors of steel reinforced concrete and steel tube concrete, a pull-out mechanics model of concrete filled square steel tubular column has been built. The slip displacement on the interface of steel and concrete of the column along the embedment length is derived by the principle of minimum potential energy. The calculation results show that the slip curves have the basic characteristics of quadratic curves distribute. The results can be used to describe the interface slips between steel and concrete under complicated loads.

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22

Yoon, K., and S. S. Rao. "Cam Motion Synthesis Using Cubic Splines." Journal of Mechanical Design 115, no. 3 (September 1, 1993): 441–46. http://dx.doi.org/10.1115/1.2919209.

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The application of minimum norm principle, similar to the principle of minimum potential energy, is presented for the general synthesis of cam motion. The approach involves the use of piecewise cubic spline functions for representing the follower displacement. The cubic splines are more convenient and simpler to use compared to general spline functions and also result in smaller peak acceleration and jerk due to the application of the minimum norm principle. A general procedure is presented for application to any cam-follower system. The effectiveness of the approach is illustrated by comparing the results given by the present method with those given by other approaches for a disk cam-translating follower.

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23

Wang, Wei Shuo, and Guang Jian Bao. "Derivation of Geometrieal Nonlinear Stiffness Matrix for Space Beam Element." Advanced Materials Research 368-373 (October 2011): 3106–12. http://dx.doi.org/10.4028/www.scientific.net/amr.368-373.3106.

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A space beam element is derived for geometrically nonlinear analysis based on the principle of minimum potential energy principle. The impact of high-order nonlinear is considered by introducing the axial deformation into the stiffness matrix. The large displacement matrix is divided into four and the initial stress matrix into three submatrix

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24

Fys, М. М., and А. L. Tserklevych. "Influence of the principle of minimum potential energy on the distribution of density and gravitational energy of the Earth for the reference model PREM." Geofizicheskiy Zhurnal 43, no. 1 (March 13, 2021): 194–210. http://dx.doi.org/10.24028/gzh.0203-3100.v43i1.2021.225549.

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From the point of view of modeling the internal structure of the Earth, its figure and evolution play an important role, which to one degree or another are associated with gravitational energy and the principle of its minimization. The realization of the minimum principle of potential for models of the distribution of the Earth’s density is the key in studies on the detection of inhomogeneous mass distribution. Achieving the minimum gravitational energy of the Earth is equivalent to the approximation of the internal structure to the hydrostatic state, and this condition is achieved due to variations in density. Therefore, for correct geophysical interpretation of gravimetric data, it is necessary to align the PREM (Preliminary Reference Earth Model) with harmonic coefficients of geopotential and minimum functional condition that determines gravitational energy, and only on this basis to estimate variations in density and tectonosphere. An algorithm for representing a piecewise continuous density distribution function in a spherical PREM model by Legendre polynomials is proposed in the paper to calculate the density, potential and energy distribution in an ellipsoidal planet using an additional condition — the minimum of gravitational energy. The use of such an algorithm made it possible to transform the spherically symmetric PREM model to a hydrostatically balanced state. It turned out that in the model obtained, the excess potential energy is concentrated in the inner and outer core of the Earth, and also insignificantly in the planet’s crust. The total energy E for the PREM reference model, which is subdivided into ellipsoidal layers, is 2.3364∙1024 erg, and in the modified PREM model after its correction for the hydrostatic component, it is 2.2828∙1024 erg. Estimation of density redistribution and identification of areas of their greatest change provide a mechanism for explaining the dynamic processes in the middle of the Earth.

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25

Li, Zhi Hui, Jun Ping Shi, and An Min Tang. "Discussions on the Two Properties and Applications of Elastic Deformation and Deformation Energy." Advanced Materials Research 250-253 (May 2011): 232–37. http://dx.doi.org/10.4028/www.scientific.net/amr.250-253.232.

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During the process of elastic deformation, based on first law of thermodynamics, deformation energy value equals to the work done by external forces moving through elastic deformation, which can determine the amount of elastic deformation. According to second law of thermodynamics, the true deformation energy value should be the minimum of all possible deformations, which can determine the distribution rule of elastic deformation. From this, it can be realized that there are some problems existed in the derived process of the minimum potential energy principle. The total potential energy of system remains constant in all of possible elastic deformation. Applying the two characteristics of elastic deformation, a few application problems could be solved expediently.

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26

Yuan, R. L., and L. S. Wang. "Generalized Variational Principle of Plates on Elastic Foundation." Journal of Applied Mechanics 58, no. 4 (December 1, 1991): 1001–4. http://dx.doi.org/10.1115/1.2897674.

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The theory of variational principle is enhanced by using the Lagrange multiplier to establish a generalized variational principle for plates on an elastic foundation. In the first part of this paper, the principle of minimum potential energy is introduced in which the integral equation is employed as the variational constrained condition. In the second part, it is shown that the generalized variational principle with two variational functions can be established. This represents, to the authors’ knowledge, the first treatment of the variational principle with these types of equations.

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27

Wang, You Kai, En Wang, and Wei Min Liang. "The Solution of Axial Symmetry Elastic Plates on a Bossinesq Subgrade with Displacement Variational Principles." Applied Mechanics and Materials 90-93 (September 2011): 2347–52. http://dx.doi.org/10.4028/www.scientific.net/amm.90-93.2347.

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The contact stress between subgrade and subgrade plate was regarded as external force to subgrade. The circular subgrade is divided into rings, and supposing that the contact stress on rings is exerted on elastic subgrade sequentially. The potential energy functions of Bossinesq subgrade are derived by using superposition theorem and Bossinesq solution of elastic mechanics. The potential energy functions were given for the whole system of subgrade, subgrade plate and external forces. The displacement and stress state can be calculated with the principle of minimum potential energy through the potential energy function of the whole system.

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28

Liu, Xiao, and Jia-wei Ye. "Heuristic algorithm based on the principle of minimum total potential energy (HAPE): a new algorithm for nesting problems." Journal of Zhejiang University-SCIENCE A 12, no. 11 (November 2011): 860–72. http://dx.doi.org/10.1631/jzus.a1100038.

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29

Bochev, Pavel, and Richard Lehoucq. "Energy Principles and Finite Element Methods for Pure Traction Linear Elasticity." Computational Methods in Applied Mathematics 11, no. 2 (2011): 173–91. http://dx.doi.org/10.2478/cmam-2011-0009.

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AbstractA conforming finite element discretization of the pure traction elasticity boundary value problem results in a singular linear system of equations. The singularity of the linear system is removed through various approaches. In this report, we consider an alternative approach in which discrete finite element formulations are derived directly from the principle of minimum potential energy. This point of view turns out to be particularly well suited to handle the rigid body modes, which are the source of the singularity in the finite element linear system. Our approach allows us to formulate a regularized potential energy principle and show that the associated weak problem is coercive in H1(Ω). This guarantees nonsingular problems, enables simplified solution algorithms and leads to more efficient and robust preconditioners for the iterative solution linear equations.

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30

Uzun, Fatih. "Form-finding and analysis of an alternative tensegrity dome configuration." Advances in Structural Engineering 20, no. 11 (February 6, 2017): 1644–57. http://dx.doi.org/10.1177/1369433216689570.

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Geiger domes are composed of cable and strut elements. This property of cable domes is the same as tensegrity structures, but in contraction to tensegrity structures, strut elements do not have a function that balances tension in cable elements with compression. In this study, a new cable dome configuration, that mimics the form of tensegrities, is proposed which is able to spread effect of an applied load into all elements of the dome and reduces its local impact. Form-finding and analysis of the Geiger and new dome configurations are performed based on the principle of minimum potential energy. Self-equilibrium forms with minimum potential energy are determined using genetic algorithms. The ability of genetic algorithm based potential energy minimization approach to perform form-finding of loaded or load free cable domes is investigated. Performance of the proposed configuration is tested and compared with the Geiger configuration under various loading conditions.

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31

Farag Ali, Ahmed, and Mohamed Moussa. "Towards Thermodynamics with Generalized Uncertainty Principle." Advances in High Energy Physics 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/629148.

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Various frameworks of quantum gravity predict a modification in the Heisenberg uncertainty principle to a so-called generalized uncertainty principle (GUP). Introducing quantum gravity effect makes a considerable change in the density of states inside the volume of the phase space which changes the statistical and thermodynamical properties of any physical system. In this paper we investigate the modification in thermodynamic properties of ideal gases and photon gas. The partition function is calculated and using it we calculated a considerable growth in the thermodynamical functions for these considered systems. The growth may happen due to an additional repulsive force between constitutes of gases which may be due to the existence of GUP, hence predicting a considerable increase in the entropy of the system. Besides, by applying GUP on an ideal gas in a trapped potential, it is found that GUP assumes a minimum measurable value of thermal wavelength of particles which agrees with discrete nature of the space that has been derived in previous studies from the GUP.

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Saad, Tony, and Joseph Majdalani. "On the Lagrangian optimization of wall-injected flows: from the Hart–McClure potential to the Taylor–Culick rotational motion." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2114 (October 21, 2009): 331–62. http://dx.doi.org/10.1098/rspa.2009.0326.

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The Taylor–Culick solution for a porous cylinder is often used to describe the bulk gas motion in idealized representations of solid rocket motors. However, other approximate solutions may be found that satisfy the same fundamental constraints. In this vein, steeper or smoother profiles may be observed in either experimental or numerical tests, particularly in the presence of intense levels of acoustic energy. In this study, we use the Lagrangian optimization principle to arrive at multiple solutions that can help to explain the practically observed motions. We then search for the extreme states that display either the least or the most kinetic energy. These are derived and found to be dependent on the chamber’s aspect ratio. By assuming a slender case, simple expressions are retrieved from which both the rotational Taylor–Culick and the irrotational Hart–McClure solutions are recovered as special cases. At the outset, a new family of flow approximations is derived extending from purely potential to highly rotational fields. These are constructed, verified and catalogued based on their kinetic energies. To help understand the tendency of a motion to shift energy states, a second law analysis is performed and used to rank these solutions based on their entropy content. Interestingly, the Taylor–Culick profile is found to represent an equilibrium state entailing the most energy and entropy among those starting from the rest. A formal extension of Kelvin’s minimum energy theorem to an open region is then pursued, followed by a direct implementation to the problem at hand. Three other flow motions with open boundaries are examined to further exemplify the application of Kelvin’s extended criteria. Our efforts illustrate the overarching harmony that exists between Lagrange’s minimization principle and Kelvin’s minimum energy theorem; both converge on the potential solution as the least kinetic energy bearer even when the velocity at the open barrier is finite.

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Song, Jia, Ce Hao, and Jiangcheng Su. "Path planning for unmanned surface vehicle based on predictive artificial potential field." International Journal of Advanced Robotic Systems 17, no. 2 (March 1, 2020): 172988142091846. http://dx.doi.org/10.1177/1729881420918461.

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The path planning for high-speed unmanned surface vehicle raises more complicated requirements to reduce sailing time and save energy. In this article, a new predictive artificial potential field is proposed using time information and predictive potential to plan a smoother path. The principle of artificial potential field with vehicle dynamics and reachability in local minimum is studied. According to global and local path planning, the most state-of-the-art traditional artificial potential field and its drawback are analysed at first. Then we proposed predictive artificial potential field with three modifications: angle limit, velocity adjustment and predictive potential to improve the feasibility and flatness of the generated path. In addition, we compare the performance between traditional artificial potential field and predictive artificial potential field, where predictive artificial potential field successfully restricts the maximum turning angle, cuts short sailing time and intelligently avoids obstacle. From the simulation results, we also verify that predictive artificial potential field can solve concave local minimum problem and enhance the reachability in special scenario. Therefore, the more reasonable path generated by predictive artificial potential field reduces sailing time and helps conserve more energy for unmanned surface vehicle.

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34

Junker, Philipp, and Klaus Hackl. "A condensed variational model for thermo-mechanically coupled phase transformations in polycrystalline shape memory alloys." Journal of the Mechanical Behavior of Materials 22, no. 3-4 (November 1, 2013): 111–18. http://dx.doi.org/10.1515/jmbm-2013-0016.

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AbstractWe derive an energy-based material model for thermomechanically coupled phase transformations in polycrystalline shape memory alloys. For the variational formulation of the model, we use the principle of the minimum of the dissipation potential for nonisothermal processes for which only a minimal number of constitutive assumptions has to be made. By introducing a condensed formulation for the representative orientation distribution function, the resulting material model is numerically highly efficient. For a first analysis, we present the results of material point calculations, where the evolution of temperature as well as its influence on the mechanical material response is investigated.

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35

Froggatt, C. D., H. B. Nielsen, R. Nevzorov, and A. W. Thomas. "Dark energy density in SUGRA models and degenerate vacua." International Journal of Modern Physics A 32, no. 17 (June 20, 2017): 1730013. http://dx.doi.org/10.1142/s0217751x17300137.

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In N[Formula: see text]=[Formula: see text]1 supergravity the tree-level scalar potential of the hidden sector may have a minimum with broken local supersymmetry (SUSY) as well as a supersymmetric Minkowski vacuum. These vacua can be degenerate, allowing for a consistent implementation of the multiple point principle. The first minimum where SUSY is broken can be identified with the physical phase in which we live. In the second supersymmetric phase, in flat Minkowski space, SUSY may be broken dynamically either in the observable or in the hidden sectors inducing a tiny vacuum energy density. We argue that the exact degeneracy of these phases may shed light on the smallness of the cosmological constant. Other possible phenomenological implications are also discussed. In particular, we point out that the presence of such degenerate vacua may lead to small values of the quartic Higgs coupling and its beta function at the Planck scale in the physical phase.

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Zhang, Wen Fu, Hai Yan Sui, Zong Wang, and Jing Ji. "Buckling Analysis of Two-Span Continuous Beams with Lateral Elastic Brace under Uniform Load." Advanced Materials Research 163-167 (December 2010): 641–45. http://dx.doi.org/10.4028/www.scientific.net/amr.163-167.641.

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Both total potential energy and buckling equation of two-span continuous beam with lateral elastic brace under uniform load are deduced, based on energy variation method and the principle of minimum potential energy. Buckling of H-beams is simulated by ANSYS software, then compared to theoretical value, validated its rationality. High precision buckling moment formula is regressed using 1stOpt which is a famous mathematical optimization analysis software in China. The relationship between lateral brace stiffness and buckling moment is obtained. Results: with lateral brace stiffness increases, critical bending moment of beam increases within up-limit, e.g. when lateral brace stiffness increases to certain extent, buckling moment no longer increases.

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Wang, Fu Li, Jing Chao Chen, and Jie Yu. "First-Principles Calculations for Electrical Proterties of the Lead Anode Plate." Advanced Materials Research 634-638 (January 2013): 1817–20. http://dx.doi.org/10.4028/www.scientific.net/amr.634-638.1817.

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Four kinds of fermi energy of lead anode plate were calculated by using first-principles. Different metals and different alloy elements of the fermi energy level were compared, the minimum electrode potential lead base alloy anode materials is known. The results calculations show that the adding alloy elements can reduce the electrode potential of the lead anode plate, four kinds of alloy systems Pb-Ag, Pb-Sb, Pb-Sr, Pb-Sn were calculated, the highest of fermi energy was Pb-Sb alloy. So the Pb-Sb alloy is expected to become the electrode potential minimum lead base alloy anode materials.

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Oguni, K., and G. Ravichandran. "An Energy-Based Model of Longitudinal Splitting in Unidirectional Fiber-Reinforced Composites." Journal of Applied Mechanics 67, no. 3 (December 7, 1999): 437–43. http://dx.doi.org/10.1115/1.1311276.

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Unidirectional fiber-reinforced composites are often observed to fail in a longitudinal splitting mode in the fiber direction under far-field compressive loading with weak lateral confinement. An energy-based model is developed based on the principle of minimum potential energy and the evaluation of effective properties to obtain an analytical approximation to the critical stress for longitudinal splitting. The analytic estimate for the compressive strength is used to illustrate its dependence on material properties, surface energy, fiber volume fraction, fiber diameter, and lateral confining pressure. The predictions of the model show good agreement with available experimental data. [S0021-8936(00)02003-1]

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Hua, Yuan, Bao Hua Lv, and Tai Quan Zhou. "Parametric Variational Principle for Solving Coupled Damage Problem." Key Engineering Materials 348-349 (September 2007): 813–16. http://dx.doi.org/10.4028/www.scientific.net/kem.348-349.813.

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The parametric variational principle adopts the extreme variational idea in the modern control theory and uses state equations deduced from the constitutive law to control the functional variation, which is an effective solution to the nonlinear equations. Based on the fundamental equations of elasto-plasticity coupled damage problem, the potential functional of elasto-plasticity is constructed. Also the state equations with approximation of damage evolution equation and load functions are constructed in the paper. The solution of elasto-plasticity damage problem can be deduced to solve problem of the minimum potential energy function under the restriction of state equations. Thus the parametric variational principle for coupled damage is proposed. The variational principle has the virtue of definite physical meaning and the finite element equations are presented in the article to facilitate the application of parametric variatioal principle, which is easy to program on computer. Using the method mentioned in the article, a numerical calculation is carried out and the calculation result shows that the method is efficient for solving elasto-plasticity damage problem.

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Psotny, Martin. "Stability Analysis of an Imperfect Slender Web Subjected to the Shear Load." Applied Mechanics and Materials 837 (June 2016): 52–57. http://dx.doi.org/10.4028/www.scientific.net/amm.837.52.

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The stability analysis of an imperfect slender web subjected to the shearing load is presented, a specialized code based on FEM has been created. The nonlinear finite element method equations are derived from the variational principle of minimum of total potential energy. To obtain the nonlinear equilibrium paths, the Newton-Raphson iteration algorithm is used. Corresponding levels of the total potential energy are defined. The peculiarities of the effects of the initial imperfections are investigated. Special attention is paid to the influence of imperfections on the post-critical buckling mode. Obtained results are compared with those gained using ANSYS system.

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Lohar, Hareram, Anirban Mitra, and Sarmila Sahoo. "Natural Frequency and Mode Shapes of Exponential Tapered AFG Beams on Elastic Foundation." International Frontier Science Letters 9 (August 2016): 9–25. http://dx.doi.org/10.18052/www.scipress.com/ifsl.9.9.

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A displacement based semi-analytical method is utilized to study non-linear free vibration and mode shapes of an exponential tapered axially functionally graded (AFG) beam resting on an elastic foundation. In the present study geometric nonlinearity induced through large displacement is taken care of by non-linear strain-displacement relations. The beam is considered to be slender to neglect the rotary inertia and shear deformation effects. In the present paper at first the static problem is solved through an iterative scheme using a relaxation parameter and later on the subsequent dynamic analysis is carried out as a standard eigen value problem. Energy principles are used for the formulation of both the problems. The static problem is solved by using minimum potential energy principle whereas in case of dynamic problem Hamilton’s principle is employed. The free vibrational frequencies are tabulated for exponential taper profile subject to various boundary conditions and foundation stiffness. The dynamic behaviour of the system is presented in the form of backbone curves in dimensionless frequency-amplitude plane and in some particular case the mode shape results are furnished.

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Su, Qiang, and Ya Ping Wu. "Influence of Compression-Flexure to Shear Lag Effect of Box Beam." Advanced Materials Research 181-182 (January 2011): 857–60. http://dx.doi.org/10.4028/www.scientific.net/amr.181-182.857.

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In this paper, the differential equations of box beams are established based on the principle of minimum potential energy and the variational method. The elastic stiffness matrix and geometric stiffness matrix considering shear lag and compression-flexure effects are induced in this paper. And a finite element program is developed. Then the influence of compression-flexure effects to shear lag effect of box beam is analyzed.

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Deng, Jia. "Study on Giant Magnetostrictive Material with Transducer Finite Element Analysis." Advanced Materials Research 700 (May 2013): 3–6. http://dx.doi.org/10.4028/www.scientific.net/amr.700.3.

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Giant magnetostrictive transducer in the work show strong magnetic mechanical coupling characteristics and nonlinear characteristics, its magnetic state and mechanical state influence each other, coupling process is very complicated, this paper according to the giant magnetostrictive material features, combined with the magnetic domain theory, establish the super magnetostrictive micro displacement actuator model, Explore stress and magnetic field changes, GMM inner magnetic strength change, and the change of strain. Join based on giant magnetostrictive actuator structure and working principle, from the principle of physics, mathematics phenomenological theory Angle to establish the combination of the mathematical model of giant magnetostrictive actuator: According to the actuator output power and output displacement, combined with the equation of motion establish output displacement - output force model. According to an internal magnetic induction intensity change, establish actuator induction voltage model; According to J-A model magnetization model. By using the finite element theory and the Hamilton principle of minimum potential energy, energy conservation principle to this mathematical model, and analyze the result.

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TAUBE, Christopher, Hans-Georg TIMMLER, Marcel HELMRICH, and Guido MORGENTHAL. "COUPLED THERMAL AND MECHANICAL ANALYSIS OF COMPOSITE CROSS SECTIONS USING MATHEMATICAL OPTIMIZATION STRATEGIES." Engineering Structures and Technologies 9, no. 1 (March 27, 2017): 41–51. http://dx.doi.org/10.3846/2029882x.2017.1299965.

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In the present article an alternative approach for the coupled thermal and mechanical analysis of composite cross sections under temperature effects is introduced, which uses the mathematical optimization as a consistent methodical base. By applying the principle of the virtual source energy for the thermal and the principle of the minimum of the total potential energy for the mechanical analysis, an accurate determination of temperature fields as well as residual strain and stress distributions is possible. The coupling is enabled by the thermal strains, which are determined based on the temperature field and passed to the nonlinear mechanical analysis as tension free pre-strains. The energy functional of the heat conduction problem is derived and implemented. The resulting optimization task is strictly convex and represents an implicit formulation, which does not impose any stability criteria. The performance of the introduced method is demonstrated on a principle example and an outlook is given on possible further extensions and applications.

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Li, Yu, Ming Fu Fu, and Zhi Long Xie. "Generalized Variation Problem of the Fractured Rock Mass under the Linear Elastic Unloading Stage." Applied Mechanics and Materials 170-173 (May 2012): 390–94. http://dx.doi.org/10.4028/www.scientific.net/amm.170-173.390.

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First, the constitutive equation of the linear elastic and the basic equations flexibility of the unloading rock mass were introduced, and then using the equations and the boundary conditions the variation principle was contracture. Prior to construct an appropriate minimum potential energy functional, on this basis, pending the introduction of two Lagrange multipliers, and absorb the variation constraints to establish the new functional. Last will 、、、as an independent variable, considering the variation stationary conditions functional of the new functional can identify the Lagrange multipliers 、 to be determined, so can build the generalized variation principle of dual variables

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Yue, Yu Ping, and Rong Zheng Cui. "The Research of Box Beam Warping Displacement Function." Applied Mechanics and Materials 578-579 (July 2014): 868–71. http://dx.doi.org/10.4028/www.scientific.net/amm.578-579.868.

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Based on the principle of minimum potential energy, choosing warping displacement function of parabolic displacement mode, using energy variational method to deduce Box beam shear lag effect analysis of differential equation to obtain shear lag warping stress. Through the calculation of simply supported box girder model and the analyse of the stress of Wide cantilever plate, box girder roof and box girder floor Assume a new warping displacement function. Through the analysis of measured results proved the rationality of this article assumes and research value.

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47

Psotný, Martin. "Nonlinear Analysis of Buckling & Postbuckling." Transactions of the VŠB – Technical University of Ostrava, Civil Engineering Series. 14, no. 1 (June 1, 2014): 75–80. http://dx.doi.org/10.2478/tvsb-2014-0010.

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Abstract The stability analysis of slender web loaded in compression was presented. To solve this problem, a specialized computer program based on FEM was created. The nonlinear finite element method equations were derived from the variational principle of minimum of potential energy. To obtain the nonlinear equilibrium paths, the Newton-Raphson iteration algorithm was used. Corresponding levels of the total potential energy were defined. The peculiarities of the effects of the initial imperfections were investigated. Special attention was focused on the influence of imperfections on the post-critical buckling mode. The stable and unstable paths of the nonlinear solution were separated. Obtained results were compared with those gained using ANSYS system.

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48

DEEP, Kusum, Shashi BARAK, Vinod Kumar KATIYAR, and Atulya Kumar NAGAR. "Minimization of Molecular Potential Energy Function Using newly developed Real Coded Genetic Algorithms." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 2, no. 1 (December 16, 2011): 51–58. http://dx.doi.org/10.11121/ijocta.01.2012.0044.

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The problem of finding the global minimum of molecular potential energy function is very challenging for algorithms which attempt to determine global optimal solution. The principal difficulty in minimizing the molecular potential energy function is that the number of local minima increases exponentially with the size of the molecule. The global minimum of the potential energy of a molecule corresponds to its most stable conformation, which dictates majority of its properties. In this paper the efficiency of four newly developed real coded genetic algorithms is tested on the molecular potential energy function. The minimization of the function is performed on an independent set of internal coordinates involving only torsion angles. Computational results with up to 100 degrees of freedom are presented.

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Li, Jingyuan, and Zifeng Li. "The Presence of a Revolution Load and Its Rotational Speed of Half the Speed of the Journal Are Necessary Conditions for the Half-Frequency Whirl of Radial Bearings." Applied Physics Research 8, no. 2 (February 15, 2016): 16. http://dx.doi.org/10.5539/apr.v8n2p16.

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<p class="1Body">In the radial sliding bearing lubrication theory, the half-frequency whirl phenomena are commonly introduced. However, the correlation of the half-frequency whirl theory with the measured resonance phenomenon is low. This paper studies the establishment of the half-frequency whirl theory, and finds that while researchers are aware of the half-frequency whirl, they disregard the necessary conditions of its occurrence. If there is no revolution load, then the half-frequency whirl does not comply with the principle of minimum potential energy. If it does not conform to the principle of minimum energy dissipation, then the half-frequency whirl does not exist. Only when the revolution load exists and its speed is half the speed of the journal will the half frequency whirl occur. Engineering oil whip results from the vibration of the rotating system. A precise radial sliding bearing lubrication theory should use cylindrical coordinates, consider the compressibility of the liquid, and consider the surface shear stress in the journal bearing capacity calculations.</p>

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Yazyev, Serdar, Anastasia Lapina, Ivan Zotov, Anton Chepurnenko, and Irina Doronkina. "Improving the energy method for calculating beams with a narrow rectangular section on the side buckling." E3S Web of Conferences 164 (2020): 02033. http://dx.doi.org/10.1051/e3sconf/202016402033.

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We propose an improved version of the energy method in calculating rectangular beams for the stability of a flat bending shape. The essence of this variant of the method is to use the principle of the minimum total energy instead of the condition for the equality of the potential strain energy and the work of external forces. This version of the method makes it easy to obtain a numerical-analytical solution for any number of members of series. The solution of the problem for a pivotally supported beam is presented taking into account the vertical displacement of the load relative to the center of gravity.

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