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Journal articles on the topic 'Equation statics'

Author: Grafiati

Published: 28 May 2022

Last updated: 30 July 2025

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1

Zhao, Jing-Shan, Xiao-Cheng Sun, and Song-Tao Wei. "Kinematics and Statics of the Gough-Stewart Platform." Applied Sciences 13, no. 18 (2023): 10150. http://dx.doi.org/10.3390/app131810150.

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This paper presents an algorithm for the kinematics and statics analysis of a Gough–Stewart platform. Through defining the velocity screw, the relative angular and linear velocities of a single rigid body can be expressed as a single vector. The velocity screw equations of various mechanisms are deduced in detail, the forward and inverse kinematics of a parallel mechanism can be solved through the velocity screw equation. Similarly, the definition of the force screw allows all constraint forces and torques of a single rigid body to be expressed using a single vector, and the static screw equat

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2

Basheleishvili, M. "The Three-Dimensional Problem of Statics of the Elastic Mixture Theory with Displacements Given on the Boundary." gmj 6, no. 6 (1999): 517–24. http://dx.doi.org/10.1515/gmj.1999.517.

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Abstract The first three-dimensional boundary value problem is considered for the basic equations of statics of the elastic mixture theory in the finite and infinite domains bounded by the closed surfaces. It is proved that this problem splits into two problems whose investigation is reduced to the first boundary value problem for an elliptic equation which structurally coincides with an equation of statics of an isotropic elastic body. Using the potential method and the theory of Fredholm integral equations of second kind, the existence and uniqueness of the solution of the first boundary val

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3

Basheleishvili, M. "Application of Analogues of General Kolosov–Muskhelishvili Representations in the Theory of Elastic Mixtures." gmj 6, no. 1 (1999): 1–18. http://dx.doi.org/10.1515/gmj.1999.1.

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Abstract The existence and uniqueness of a solution of the first, the second and the third plane boundary value problem are considered for the basic homogeneous equations of statics in the theory of elastic mixtures. Applying the general Kolosov–Muskhelishvili representations from [Basheleishvili, Georgian Math. J. 4: 223–242, 1997], these problems can be splitted and reduced to the first and the second boundary value problem for an elliptic equation which structurally coincides with the equation of statics of an isotropic elastic body.

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4

Wang, Shao Feng. "A unified dislocation equation from lattice statics." Journal of Physics A: Mathematical and Theoretical 42, no. 2 (2008): 025208. http://dx.doi.org/10.1088/1751-8113/42/2/025208.

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5

Ferguson, Robert J. "Efficient simultaneous wave-equation statics and trace regularization by series approximation." GEOPHYSICS 75, no. 3 (2010): U19—U28. http://dx.doi.org/10.1190/1.3388468.

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To address the problems of irregular trace spacing and statics correction, simultaneous regularization and wave-equation statics (WE statics) are implemented by least-squares inversion. In general, inversion is found to be intractable in three dimensions, so series approximation is made to reduce significantly the number of required integrals. The resulting operator is suitable for direct inversion or for use with gradient methods. Real and synthetic data are used to determine the viability of the inversion. For synthetic data, even for severe velocity variation and topography, inversion conve

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6

Wu, Yao Hua. "Based on Quadratic Equations of Tyre Lifting Mechanism before Connecting Rod Combined-Type Modeling Method." Advanced Materials Research 529 (June 2012): 190–94. http://dx.doi.org/10.4028/www.scientific.net/amr.529.190.

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The method of using two equations, a push connecting rod type dump before lifting mechanism of mathematical model, the use of mathematical and mechanical knowledge, establishing geometric equations, establish the statics equation, calculation and analysis, solution binary quadratic equations, get oil cylinder's thrust, and thus for study, so as to further optimized.

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7

Anderson, James E., and Eric van Wincoop. "Gravity with Gravitas: A Solution to the Border Puzzle." American Economic Review 93, no. 1 (2003): 170–92. http://dx.doi.org/10.1257/000282803321455214.

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Gravity equations have been widely used to infer trade flow effects of various institutional arrangements. We show that estimated gravity equations do not have a theoretical foundation. This implies both that estimation suffers from omitted variables bias and that comparative statics analysis is unfounded. We develop a method that (i) consistently and efficiently estimates a theoretical gravity equation and (ii) correctly calculates the comparative statics of trade frictions. We apply the method to solve the famous McCallum border puzzle. Applying our method, we find that national borders redu

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Schneider, William A., Lindy D. Phillip, and Ernest F. Paal. "Wave‐equation velocity replacement of the low‐velocity layer for overthrust‐belt data." GEOPHYSICS 60, no. 2 (1995): 573–79. http://dx.doi.org/10.1190/1.1443795.

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Seismic land data are commonly plagued by nonhyperbolic distortions induced by a variable near‐surface, low‐velocity layer (LVL). First‐arrival refraction analysis is conventionally employed to estimate the LVL geometry and velocities. Then vertical static time shifts are used to replace the LVL velocities with the more uniform, faster velocities that characterize the underlying refracting layer. This methodology has earned a good reputation as a geophysical data processing tool; however, velocity replacement with static shifts assumes that no ray bending occurred at the LVL base and that wave

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9

Čaklović, Koraljka, and Lavoslav Čaklović. "Computation of residual statics using projectors." GEOPHYSICS 50, no. 9 (1985): 1502–4. http://dx.doi.org/10.1190/1.1442018.

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The residual statics problem, as we know, is treated as the solution of one linear system of equations. If we assume that the static corrections are “surface consistent,” then we know that time shifts of each trace can be written as the sum of three terms [Formula: see text] where i = 1, …, [Formula: see text] is the shot position index with [Formula: see text] the number of shot positions, j = 1, …, [Formula: see text] is the receiver position index with [Formula: see text] the number of receiver positions, k = 1, …, [Formula: see text] is the common‐depth‐point (CDP) position index with [For

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10

Chen, Li Wen, Bing Yan Cui, Zhi Jun Wang, Ling Chao Meng, and Zhan Xian Li. "Statics Analysis and Design of the 6-DOF Lower Limb Bionic Leg." Journal of Biomimetics, Biomaterials and Biomedical Engineering 26 (February 2016): 1–12. http://dx.doi.org/10.4028/www.scientific.net/jbbbe.26.1.

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In order to improve ability of walking and crossing the barriers , increase the carrying capacity, and enhance its popularity and adaptability, a novel lower limb bionic leg is presented based on 3-UPS parallel mechanism, which has the characteristics of movement flexible and strong adaptability. It is very important analysis to statics of lower limb bionic leg. Firstly, statics equation of the lower limb bionic leg of driving force and output force is established based on virtual work principle. Secondly, static performance evaluation index is defined and the evaluation index distribution map

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Cui, Bing Yan, Li Wen Chen, Zhi Jun Wang, Yuan Hao Zhao, Li Zhan Xian, and Zhen Lin Jin. "Analysis of Statics and Design of Structur Parameters for a Bionic Robot Hip Joint." Journal of Biomimetics, Biomaterials and Biomedical Engineering 22 (March 2015): 3–12. http://dx.doi.org/10.4028/www.scientific.net/jbbbe.22.3.

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The hip joint is one of the body's important joints, most of the lower limb activities of the human body are inseparable from the hip joint, a novel bionic robot hip joint was proposed based on 3-DOF spherical parallel mechanism. The statics performance of the bionic robot hip joint was analyzed, and the structure parameters were designed. First, the static transmission equation of the bionic robot hip joint was established using the principle of virtual works, which simplifies the calculation process of the bionic robot hip joint. Further, using the norm in Matrix theory, the force Jacobian m

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12

AGUERO RUBIO, JOSE, JAVIER LÓPEZ MARTÍNEZ, MARTA GOMEZ GALAN, and ANGEL JESUS CALLEJÓN FERRE. "GRAPHIC METHOD USING A SYSTEM OF ARTICULATED LINKS TO CALCULATE THE STATIC RESPONSE OF SUSPENDED CABLES." DYNA 100, no. 2 (2025): 102–6. https://doi.org/10.52152/d11302.

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This paper presents a method for studying the static response in suspended cables. A novel discretization technique based on Archimedes' methods is applied, which results in a graphic resolution of the problem based on a system of articulated bars, and which defines a finite cable element. Parabolic approximation of the cable is studied. The proposed model allows manual calculation. It can solve the problem via three iterations whose equations are drawn from intuitive graphics and with errors less than 2% from the first iteration. Therefore, it represents an important didactic innovation both

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13

De Tommasi, D., and S. Marzano. "Statics of Edge Cables in Tent Structures." International Journal of Space Structures 3, no. 1 (1988): 15–19. http://dx.doi.org/10.1177/026635118800300102.

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The edge cable configurations for tent structures in the prestressed state are analyzed. We show that these configurations identify with the characteristic lines associated with differential equation of the membrane equilibrium written in terms of the stress function. Moreover, existence and uniqueness for the equilibrium problem of membrane are proved in a special case.

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14

Liu, Xiang, Jingshan Zhao, Jie Zhang, and Wei Chen. "Elastokinematics of a rectilinear rear independent suspension." Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 230, no. 14 (2016): 1904–24. http://dx.doi.org/10.1177/0954407015625143.

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The rectilinear rear independent suspension investigated in this paper benefits from its excellent kinematic characteristics. Because of the over-constraints of the rectilinear rear independent suspension as a rigid-flexible coupled multi-body system, its elastokinematics are heavily dependent on the compliance characteristics. This paper proposes an efficient approach to establish its elastokinematic model based on the transfer matrix method. First, the overall system transfer equation of the rectilinear rear independent suspension is established. Then, the statics equation is obtained by int

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15

Khan, Adnan, Muhammad Imran Liaqat, and Asma Mushtaq. "Analytical Analysis for Space Fractional Helmholtz Equations by Using The Hybrid Efficient Approach." Acta Mechanica et Automatica 18, no. 4 (2024): 116–25. http://dx.doi.org/10.2478/ama-2024-0065.

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Abstract The Helmholtz equation is an important differential equation. It has a wide range of uses in physics, including acoustics, electro-statics, optics, and quantum mechanics. In this article, a hybrid approach called the Shehu transform decomposition method (STDM) is implemented to solve space-fractional-order Helmholtz equations with initial boundary conditions. The fractional-order derivative is regarded in the Caputo sense. The solutions are provided as series, and then we use the Mittag-Leffler function to identify the exact solutions to the Helmholtz equations. The accuracy of the co

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16

Han, Xu Zhao, Yu Mei Huang, Chun Chen, Hong Yan Liu, and Xing Fang Yang. "Kinematics and Statics Analysis of a 2-DOF Planar Parallel Mechanism with over Constraint." Advanced Materials Research 261-263 (May 2011): 913–17. http://dx.doi.org/10.4028/www.scientific.net/amr.261-263.913.

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This paper presents a deep research on 2-DOF planar parallel mechanism during developing a new type of hybrid machine tool. The composition of this planar parallel mechanism is introduced, its direct and inverse kinematics solution equations as well as the solution equations for the speed and the acceleration are deduced, meanwhile, the jacobian matrix is obtained. The statics problems of the parallel mechanism are modeled and analyzed based on principle of virtual work, and the balancing driving force solution equation of the driving part is given. Through the solving process we can see that

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17

Zheming, Z., and S. Wenkang. "Statics of Gas-Lubricated Slider Bearings in Magnetic Recording Disk Files." Proceedings of the Institution of Mechanical Engineers, Part C: Mechanical Engineering Science 206, no. 1 (1992): 13–17. http://dx.doi.org/10.1243/pime_proc_1992_206_090_02.

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This paper presents theoretical and experimental analyses of the static characteristics of gas-lubricated slider bearings. An implicit scheme, based on the Patankar-Spalding method, which is commonly utilized in the numerical heat transfer and fluid flow, is developed for the numerical solution of the Reynolds equation. Further investigations on the steady static minimum flying height and the pitch angle are presented by use of a transient response analysis. Theoretical results are experimentally verified to be correct and reliable. By comparing a grooved slider with a non-grooved one in the s

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18

Doppel, K., and R. Hochmuth. "A nonlinear singular integral equation model for hysteresis in magneto-statics." IEEE Transactions on Magnetics 32, no. 3 (1996): 678–81. http://dx.doi.org/10.1109/20.497329.

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19

Costa, Gustavo, Pierre Rossi, Mariane Rita, Eduardo Fairbairn, and Fernando Ribeiro. "Use of a Semi-Explicit Probabilistic Numerical Model for Concrete Cracking: From Static to Dynamic Loadings." Applied Sciences 14, no. 22 (2024): 10643. http://dx.doi.org/10.3390/app142210643.

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In this paper, concrete cracking is investigated in dynamics through finite element modeling. A probabilistic semi-explicit model, previously developed and validated for static loading, is extended for dynamic loading. The model in statics is based on two material mechanical parameters: the tensile strength and the critical strain-energy release rate in mode I, GIC, of the Linear Elastic Fracture Mechanics (LEFM) theory. Concerning the dynamic aspects of the model, the tensile strength rate effect is modeled by an empirical dynamic-to-static strength ratio (Dynamic Increase Factor—DIF) and a s

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20

Hu, Bo, Yi Lu, Xiuli Zhang, and Jianping Yu. "Unified analysis of statics of some limited-DOF parallel manipulators." Robotica 30, no. 3 (2011): 333–42. http://dx.doi.org/10.1017/s0263574711000634.

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SUMMARYAn observation approach is proposed for determining the poses of the active/constrained wrench and the unified statics of some limited-DOF parallel manipulators (PMs) are studied systematically. First, a general PM model is constructed, and the unified inverse displacement is analyzed. Second, various types of acceptable legs are synthesized; the poses of the active/constrained wrench exerted on the various acceptable legs are determined by the observation approach. Third, a unified 6 × 6 Jacobina matrix and a unified statics equation are derived for solving active/constrained wrench of

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21

Vincent, Olivier, and Philippe Marmottant. "On the statics and dynamics of fully confined bubbles." Journal of Fluid Mechanics 827 (August 18, 2017): 194–224. http://dx.doi.org/10.1017/jfm.2017.487.

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We investigate theoretically the statics and dynamics of bubbles in fully confined liquids, i.e. in liquids surrounded by solid walls in all directions of space. This situation is found in various natural and technological contexts (geological fluid inclusions, plant cells and vessels, soil tensiometers, etc.), where such bubbles can pre-exist in the trapped liquid or appear by nucleation (cavitation). We focus on volumetric deformations and first establish the potential energy of fully confined bubbles as a function of their radius, including contributions from gas compressibility, surface te

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22

Sun, Jun-Yi, Qi Zhang, Ji Wu, Xue Li, and Xiao-Ting He. "Large Deflection Analysis of Peripherally Fixed Circular Membranes Subjected to Liquid Weight Loading: A Refined Design Theory of Membrane Deflection-Based Rain Gauges." Materials 14, no. 20 (2021): 5992. http://dx.doi.org/10.3390/ma14205992.

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The anticipated use of elastic membranes for deflection-based rain gauges has provided an impetus for this paper to revisit the large deflection problem of a peripherally fixed circular membrane subjected to liquid weight loading, a statics problem when the fluid–structure interaction of membrane and liquid reaches static equilibrium. The closed-form solution of this statics problem of fluid–structure interaction is necessary for the design of such membrane deflection-based rain gauges, while the existing closed-form solution, due to the use of the small rotation angle assumption of the membra

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23

Adamowicz, Krzysztof. "The unresolved problem of determining the forest interest rate." Folia Forestalia Polonica 60, no. 2 (2018): 122–30. http://dx.doi.org/10.2478/ffp-2018-0012.

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Abstract Valuation of forests and their components is a significant problem, both for science and practice. At present, in many countries, the market of forest property is limited. As a result, no conclusions may be inferred on the forest value based on the information on forest purchase and sale transactions. In this situation, we apply static methods of forest valuation. The problem of forest statics has been discussed for years (e.g., Brukas et al. 2001; Chang 1983, 2001; Dieter 2001; Hartman 1976; Manley and Bare 2001; Mohring 2001; Zhang 2001; Viitala 2016). Static methods of forest valua

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Krzysztof, Adamowicz. "The unresolved problem of determining the forest interest rate." FOLIA FORESTALIA POLONICA, SERIES A – FORESTRY 60, no. 2 (2018): 122–30. https://doi.org/10.2478/ffp-2018-0012.

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Valuation of forests and their components is a significant problem, both for science and practice. At present, in many countries, the market of forest property is limited. As a result, no conclusions may be inferred on the forest value based on the information on forest purchase and sale transactions. In this situation, we apply static methods of forest valuation. The problem of forest statics has been discussed for years (e.g., Brukas et al. 2001; Chang 1983, 2001; Dieter 2001; Hartman 1976; Manley and Bare 2001; Mohring 2001; Zhang 2001; Viitala 2016). Static methods of forest valuation are

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25

Lin, Zone Ching, and Jia Rong Ye. "Two Dimensional Quasi-Steady Molecular Statics Nanocutting Simulation for Cutting Copper Material with Point Defect." Advanced Materials Research 264-265 (June 2011): 1357–63. http://dx.doi.org/10.4028/www.scientific.net/amr.264-265.1357.

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This article presents a quasi-steady molecular statics nanocutting simulation model for simulating orthogonal two dimension cutting copper materials with different point defects by using diamond cutters. The analyses of cutting action, cutting force, equivalent strain and equivalent stress are taken during nanocutting copper material with point defect. The two dimensional quasisteady molecular statics nanocutting model first assumes the trajectory of each atom of copper workpiece being cut whenever the diamond cutter goes forward one step. It then uses the Hooke- Jeeves search method to solve

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Mikesell, T. Dylan, Kasper van Wijk, Elmer Ruigrok, Andrew Lamb, and Thomas E. Blum. "A modified delay-time method for statics estimation with the virtual refraction." GEOPHYSICS 77, no. 6 (2012): A29—A33. http://dx.doi.org/10.1190/geo2012-0111.1.

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Topography and near-surface heterogeneities lead to traveltime perturbations in surface land-seismic experiments. Usually, these perturbations are estimated and removed prior to further processing of the data. A common technique to estimate these perturbations is the delay-time method. We have developed the “modified delay-time method,” wherein we isolate the arrival times of the virtual refraction and estimate receiver-side delay times. The virtual refraction is a spurious arrival found in wavefields estimated by seismic interferometry. The new method removes the source term from the delay-ti

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27

Song, Chongmin. "A matrix function solution for the scaled boundary finite-element equation in statics." Computer Methods in Applied Mechanics and Engineering 193, no. 23-26 (2004): 2325–56. http://dx.doi.org/10.1016/j.cma.2004.01.017.

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28

Kaletnіk, Grigory, and Oleh Tsurkan. "STATIC CONDITIONS OF A LOOSE ENVIRONMENT IN SOLVING THE TASKS OF ITS VIBROMOVEMENT." Vibrations in engineering and technology, no. 4(95) (December 20, 2019): 5–15. http://dx.doi.org/10.37128/2306-8744-2019-4-1.

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The method of formalizing a granular medium in the form of a continuous deformable medium provides that the granular medium is continuous. In this case, the methods of mechanics of continuous deformable media in Eulerian or Lagrangian coordinates are used. The method allows you to take into account the interaction between particles in the form of elastic, viscous or plastic components of internal resistance. With this formalization, the most widespread application of the Navier-Stokes equation. Unfortunately, the exact correct solution of such an equation in an analytical form does not exist.

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29

Xia, Yan, Rong Qiang Liu, Hong Wei Guo, and Zong Quan Deng. "Design and Analysis of an Under-Actuated Self-Adaptive Mechanical Hand." Applied Mechanics and Materials 602-605 (August 2014): 1083–89. http://dx.doi.org/10.4028/www.scientific.net/amm.602-605.1083.

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A kind of under-actuated self-adaptive mechanical hand was developed in this paper. This mechanical hand consists of three 3-dof under-actuated fingers, and four motors are adopted to drive nine joints. The hand has self-adaptation to targets in different shapes and sizes and it can perform actions, such as folding, unfolding and grasping. In addition, a quasi-statics model of the 3-dof under-actuated finger was established in this paper. The relationship equation between the grasping forces and the driving and damping torques was obtained, and the influence of target size and driving torques

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Sun, Jian Gang, Tie Jun Li, Xue Sen Zhang, and Mei Ying Chen. "The Research on the Dynamics of High-Speed Friction and Wear Test System in Mechanical Engineering." Advanced Materials Research 644 (January 2013): 326–32. http://dx.doi.org/10.4028/www.scientific.net/amr.644.326.

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By researching the dynamics of high speed friction and wear test system, establish the statics and dynamics model of high-speed dial and get the equation of motion of turntable scrapers state. Using Ansys Workbench software platform analysis the order modal of the turntable, get the kinetic parameters of the system. Some suggestion and methods are proposed on avoiding vibration of turntable system.

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Ibănescu, Radu, and Cătălin Ungureanu. "Approach of a Particle Statics Problem by Using the Bond-Graph Modeling Method." Applied Mechanics and Materials 657 (October 2014): 599–603. http://dx.doi.org/10.4028/www.scientific.net/amm.657.599.

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The paper presents a new approach to the numerical solution of a particle in equilibrium lying on a circle and subjected to the action of a linear spring. The difficulties of solving such a problem and the Mathcad and Simulink based solutions are presented in [1, 2, 3]. The most important difficulties consist in symbolically solving a forth degree trigonometric equation or in solving a complicated trigonometric inequality. This is why a numerical solution is preferred. The use of the bond graph modelling method for solving this problem of equilibrium is presented in this paper. The bond-graph

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Malko, O. G., O. V. Kuchmustenko, M. V. Shavranskyi, T. O. Vavruk, and O. S. Tcareva. "SIMULATION OF QUASISTATATICS OF THE PROCESS OF FORMATION OF A LIQUID MENISK TYPE OF HANGING DROP ON THE SUBJECT OF METHODOLOGICAL PROVISION OF MEASUREMENT." METHODS AND DEVICES OF QUALITY CONTROL, no. 1(46) (June 28, 2021): 33–42. http://dx.doi.org/10.31471/1993-9981-2021-1(46)-33-42.

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A mathematical model has been developed for describing a capillary surface of the hanging drop type in the form of a system of fifth-order nonlinear differential equations, which corresponds to five geometric characteristics of the meniscus: the distance from the meniscus axis to a given point on the capillary surface, the distance from the plane normal to the meniscus surface at an umbilical point to a given point on capillary surface, the angle between the axis of symmetry and the normal to the capillary surface at a given point, the area and volume of the capillary surface bounded by a cut

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Bokov, Igor, Natalia Bondarenko, and Elena Strelnikova. "INVESTIGATION OF STRESS-STRAIN STATE OF TRANSVERSELY ISOTROPIC PLATES UNDER BENDING USING EQUATION OF STATICS {1,2} –APPROXIMATION." EUREKA: Physics and Engineering 5 (September 30, 2016): 58–66. http://dx.doi.org/10.21303/2461-4262.2016.00159.

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The study examined the construction of the fundamental solution for the equations of statics {1,2} – approximation for transversely isotropic plates under bending with the action of concentrated force. Equations {1,2} -approximation were obtained by the decomposition method in the thickness coordinate using the Legendre polynomials. These equations take into account all the components of the stress tensor, including the transverse shear and normal stresses. Since the classical theory of Kirchhoff-Love doesn’t take account of these stresses, the study on the basis of refined theories of stress-

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Krutii, Yurii, Mykola Surianinov, and Vitalii Chaban. "The Solution of the Shells Theory Problems by the Numerical-Analytical Boundary Elements Method." Materials Science Forum 968 (August 2019): 460–67. http://dx.doi.org/10.4028/www.scientific.net/msf.968.460.

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The application of the numerical-analytical boundary elements method (NA BEM) to the calculation of shells is considered. The main problem here is due to the fact that most of the problems of statics, dynamics and stability of shells are reduced to solving an eighth-order differential equation. As a result, all analytical expressions of the NA BEM (fundamental functions, Green functions, external load vectors) turn out to be very cumbersome, and intermediate transformations are associated with eighth-order determinants. It is proposed along with the original differential equation to consider a

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Hsieh, Long Chang, and Tzu Hsia Chen. "On the Kinematics and Statics of Planetary Simple Gear Reducers." Advanced Materials Research 591-593 (November 2012): 2165–68. http://dx.doi.org/10.4028/www.scientific.net/amr.591-593.2165.

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The power system equipped in machinery contains power source (motor or engine) and gear reducer to get large output torque. The rotation speed of motor is made higher and higher to attach high power with the same volume. Hence, the reduction ratio of gear reducer is required to be higher and higher. Planetary gear trains can be used as the gear reducers with high reduction ratio. However, the planetary gear train with high reduction ratio is compound gear system. This paper proposes planetary simple gear reducers with high reduction ratio. According to train value equation, the kinematic desig

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36

Rajasekaran, Sara, and George A. McMechan. "Prestack processing of land data with complex topography." GEOPHYSICS 60, no. 6 (1995): 1875–86. http://dx.doi.org/10.1190/1.1443919.

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A new wave‐equation–based prestack seismic processing system is proposed. This system has only two essential elements; velocity analysis and depth migration. This approach applies truly surface‐consistent statics corrections, regardless of the amount of elevation, change or of near‐surface velocity variation. It uses tomography for estimating the details of shallow velocities and a finite‐difference solution of the two‐way wave‐equation both for computation of image times and for data extrapolation in migration. A field data set that violates most of the assumptions in conventional common midp

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Zhu, Xianhuai, Burke G. Angstman, and David P. Sixta. "Overthrust imaging with tomo‐datuming: A case study." GEOPHYSICS 63, no. 1 (1998): 25–38. http://dx.doi.org/10.1190/1.1444319.

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Through the use of iterative turning‐ray tomography followed by wave‐equation datuming (or tomo‐datuming) and prestack depth migration, we generate accurate prestack images of seismic data in overthrust areas containing both highly variable near‐surface velocities and rough topography. In tomo‐datuming, we downward continue shot records from the topography to a horizontal datum using velocities estimated from tomography. Turning‐ray tomography often provides a more accurate near‐surface velocity model than that from refraction statics. The main advantage of tomo‐datuming over tomo‐statics (tom

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Koreneva, Elena, and Valery Grosman. "EQUATION DECOMPOSITION METHOD FOR SOLVING OF PROBLEMS OF STATICS, VIBRATIONS AND STABILITY OF THIN-WALLED CONSTRUCTIONS." International Journal for Computational Civil and Structural Engineering 16, no. 2 (2020): 63–70. http://dx.doi.org/10.22337/2587-9618-2020-16-2-63-70.

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The work suggests the effective equation decomposition method (EDM) for solving of statics, vibrations and stability problems of thin-walled constructions. This method is based on the partition of the initial problem on the consideration of more simple auxiliary problems. The additional unknown functions are introduced for definition of the sought solutions. The paper shows the method’s advantages on the examples of the boundary value problems for rectangular areas. The problem of anisotropic plate resting on an elastic subgrade and subjected to an action of expanding forces acting in the midd

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Ebikiton, Ndiwari, and Ongodiebi Zuonaki. "Time Impact on Residue in a Non - homogeneous Equation of Statics in the Theory of Elastic Mixture." International Journal of Mathematics And Computer Research 09, no. 05 (2021): 2303–8. https://doi.org/10.47191/ijmcr/v9i5.04.

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Residual stress in continuum has not been quantified because time relationship with residues has not been proven analytically. This is achieved in this paper by analyzing a two component mixture with the non-homogeneous equation of statics in the theory of elastic mixture, and second order differentialequations with variable coefficients. A dry mixture of sand and cement is transformed into acontinuum, which is been determined as an entire or a meromorphic function, as a result of the existence of residues that are contained in the principal component of the mixture obtained directly from the

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Curtis, Andrew, and Johan O. A. Robertsson. "Volumetric wavefield recording and wave equation inversion for near‐surface material properties." GEOPHYSICS 67, no. 5 (2002): 1602–11. http://dx.doi.org/10.1190/1.1512751.

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“Volumetric recording” of the seismic wavefield implies that the local receiver group or array approximately encloses a volume of the earth. We show how volumetric recording can be used to measure several spatial derivatives of the wavefield. By making use of the full elastic wave equation, the free surface condition on elastic wavefields, and derivative centering techniques analagous to Lax‐Wendroff corrections used in synthetic finite‐difference modeling, these derivative estimates can be inverted for P‐ and S‐velocities in the near surface directly beneath the receiver group. The quantities

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Li, Huai Yong, Su Jing Wang, Ying Xun Guo, and Jian Hua Huang. "Mechanical Analysis of the Arm Lifting Rope of the Dynamic Compaction Machine." Applied Mechanics and Materials 851 (August 2016): 259–64. http://dx.doi.org/10.4028/www.scientific.net/amm.851.259.

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In this paper, the mechanics equation of the dynamic compaction machine arm frame is established based on the theory of statics, the arm lifting rope force is given, the influence of the wire rope force with relative position parameters changing is also discussed. The critical factors that affect the arm lifting rope force are identified. Compared the simulation and the test results, the major forces errors are less than 8%. The correctness of the theoretical study and simulation are verified. The research results could be used for the arm wire rope type selection of the dynamic compaction.

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Tewary, V. K., and E. R. Fuller. "Lattice statics Green's function method for calculation of atomistic structure of grain boundary interfaces in solids: Part II. Anharmonic theory." Journal of Materials Research 4, no. 2 (1989): 320–26. http://dx.doi.org/10.1557/jmr.1989.0320.

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The lattice statics Green's function method for calculation of the atomistic structure of grain boundary interfaces in solids as described in Part I is extended to include anharmonic effects. It is shown that the ‘anharmonic’ response of a solid to ‘anharmonic’ forces can be represented in terms of the ‘harmonic’ response of the solid to an effective anharmonic force. The Green's function method then requires solving a finite order nonlinear matrix equation, which is done by using standard numerical methods. For the purpose of illustration, the method is applied to calculate the atomistic stru

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Andrieux, S., and H. D. Bui. "On some nonlinear inverse problems in elasticity." Theoretical and Applied Mechanics 38, no. 2 (2011): 125–54. http://dx.doi.org/10.2298/tam1102125a.

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In this paper, we make a review of some inverse problems in elasticity, in statics and dynamics, in acoustics, thermoelasticity and viscoelasticity. Crack inverse problems have been solved in closed form, by considering a nonlinear variational equation provided by the reciprocity gap functional. This equation involves the unknown geometry of the crack and the boundary data. It results from the symmetry lost between current fields and adjoint fields which is related to their support. The nonlinear equation is solved step by step by considering linear inverse problems. The normal to the crack pl

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Lin, Zone Ching, and Ying Chih Hsu. "Simulation Analysis of Nanocutting on the Surface of Sapphire." Advanced Materials Research 579 (October 2012): 184–92. http://dx.doi.org/10.4028/www.scientific.net/amr.579.184.

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The three-dimensional quasi-steady molecular statics nanocutting model developed by this paper carries out simulation analysis of nanocutting of sapphire substrate in order to explore the effects of tools with the same tip radii of probe and straight-line cutting at different cutting depths, on cutting force. The three-dimensional quasi-steady molecular statics nanocutting sapphire workpiece model first assumes the trajectory of each atom of the sapphire workpiecs being cut whenever the diamond cutter goes forward one step. It then uses the optimization search method to solve the force equilib

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Lyu, Bin, Qin Su, and Kurt J. Marfurt. "Tomographic velocity analysis and wave-equation depth migration in an overthrust terrain: A case study from the Tuha Basin, China." Interpretation 6, no. 1 (2018): T1—T13. http://dx.doi.org/10.1190/int-2017-0053.1.

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Although the structures associated with overthrust terrains form important targets in many basins, accurately imaging remains challenging. Steep dips and strong lateral velocity variations associated with these complex structures require prestack depth migration instead of simpler time migration. The associated rough topography, coupled with older, more indurated, and thus high-velocity rocks near or outcropping at the surface often lead to seismic data that suffer from severe statics problems, strong head waves, and backscattered energy from the shallow section, giving rise to a low signal-to

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Koleková, Y., M. Petronijević, and G. Schmid. "Special dynamic soilstructure analysis procedures demonstrated for two tower-like structures." Slovak Journal of Civil Engineering 18, no. 2 (2010): 26–33. http://dx.doi.org/10.2478/v10189-010-0008-2.

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Special dynamic soilstructure analysis procedures demonstrated for two tower-like structuresMany problems in Earthquake Engineering require the modeling of the structure as a dynamic system including the sub-grade. A structural engineer is usually familiar with the Finite Element Method but has a problem modeling the sub-grade when its infinite extension and wave propagation are the essential features. If the dynamic equation of a soil-structure system is written in a frequency domain and the variables of the system are total displacements, then the governing equations are given as in statics.

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Koreneva, Elena B. "ETHOD OF COMPENSATING LOADS FOR SOLVING OF ANISOTROPIC MEDIUM PROBLEMS." International Journal for Computational Civil and Structural Engineering 14, no. 1 (2018): 71–77. http://dx.doi.org/10.22337/2587-9618-2018-14-1-71-77.

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The work applies the method of compensating loads (MCL) for solution of statics and vibrations problems of plates with cylindrical anisotropy. For receiving of basic and compensating solutions Nielsen’s equation is used. The solution expressed in terms of Bessel functions is obtained. Such way can be used in con-sideration of symmetric, antisymmetric and unsymmetric flexure of orthotropic circular plates resting on an elastic Winkler’s subgrade. The similar method can be also utilized for examination of the symmetric vibrations of the orthotropic circular plates as well as for the cases of vib

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Siciliano, Bruno. "The Tricept robot: Inverse kinematics, manipulability analysis and closed-loop direct kinematics algorithm." Robotica 17, no. 4 (1999): 437–45. http://dx.doi.org/10.1017/s0263574799001678.

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This paper is aimed at presenting a study on the kinematics of the Tricept robot, which comprises a three-degree-of-freedom (dof) parallel structure having a radial link of variable length. The robot workspace is characterized and the inverse kinematics equation is obtained by using spherical coordinates. The inverse differential kinematics and statics are derived in terms of both an analytical and a geometric Jacobian, and a manipulability analysis along the various workspace directions is developed using the concept of force and velocity ellipsoids. A Jacobian-based Closed-Loop Direct Kinema

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SABIR, ZULQURNAIN, MUHAMMAD ASIF ZAHOOR RAJA, and DUMITRU BALEANU. "FRACTIONAL MAYER NEURO-SWARM HEURISTIC SOLVER FOR MULTI-FRACTIONAL ORDER DOUBLY SINGULAR MODEL BASED ON LANE–EMDEN EQUATION." Fractals 29, no. 05 (2021): 2140017. http://dx.doi.org/10.1142/s0218348x2140017x.

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This research is related to present a novel fractional Mayer neuro-swarming intelligent solver for the numerical treatment of multi-fractional order doubly singular Lane–Emden (LE) equation using combined investigations of the Mayer wavelet (MW) neural networks (NNs) optimized by the global search effectiveness of particle swarm optimization (PSO) and interior-point (IP) method, i.e. MW-NN-PSOIP. The design of novel fractional Mayer neuro-swarming intelligent solver for multi-fractional order doubly singular LE equation is derived from the standard LE model and the shape factors; fractional or

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Tewary, V. K., E. R. Fuller, and R. M. Thomson. "Lattice statics Green's function method for calculation of atomistic structure of grain boundary interfaces in solids: Part I. Harmonic theory." Journal of Materials Research 4, no. 2 (1989): 309–19. http://dx.doi.org/10.1557/jmr.1989.0309.

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A lattice statics Green's function method is described for calculating the atomistic structure of a solid near a grain boundary interface. First, a reference state is defined which is ‘near’ the equilibrium state. The Green's function for the reference state is obtained in terms of the perfect lattice Green's function by mapping the lattice sites of the reference state to the perfect lattice sites and solving the Dyson's equation within a supercell. This Green's function gives the response of the reference state which determines the atomic relaxations under the net forces which would be presen

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