A review of temporal and spatial dispersions of linear and quadratic finite elements in linear elastic wave propagation problems

Authors: Kolman, R. (Radek), Okrouhlík, M. (Miloslav), Kruisová, A. (Alena)

Source: Proceedings of the Estonian Academy of Sciences, Vol 73, Iss 3, Pp 279-316 (2024)

Subject Terms: Finite element methods applied to problems in solid mechanics, Linear elasticity with initial stresses, Science, elastic wave propagation, finite element method, direct time integration, spurious oscillations, Finite difference methods applied to problems in solid mechanics, Error bounds for initial value and initial-boundary value problems involving PDEs, Vibrations in dynamical problems in solid mechanics, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Strings, dispersion, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Linear waves in solid mechanics, PDEs in connection with mechanics of deformable solids, Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids

File Description: application/xml

Access URL: https://hdl.handle.net/11104/0358061

A Two-Level Crank-Nicolson Difference Scheme and Its Richardson Extrapolation Methods for a Magneto-Thermo-Elasticity Model: A two-level Crank-Nicolson difference scheme and its Richardson extrapolation methods for a magneto-thermo-elasticity model

Authors: Deng, Dingwen, Zhang, Ruyu

Source: Advances in Applied Mathematics and Mechanics. 16:608-635

Subject Terms: Finite difference methods for boundary value problems involving PDEs, energy conservation, Iterative numerical methods for linear systems, Extrapolation to the limit, deferred corrections, convergence, Richardson extrapolation methods, priori estimation, Symbolic computation and algebraic computation, Finite difference methods applied to problems in solid mechanics, Thermal effects in solid mechanics, Electromagnetic effects in solid mechanics, Classical linear elasticity, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, finite difference method, solvability

File Description: application/xml

Modeling and experiments on the vibro-acoustic analysis of ring stiffened cylindrical shells with internal bulkheads: A comparative study: Modeling and experiments on the vibro-acoustic analysis of ring stiffened cylindrical shells with internal bulkheads: a comparative study

Authors: Cong Gao, Jiawei Xu, Fuzhen Pang, Haichao Li, Kai Wang

Source: Engineering Analysis with Boundary Elements. 162:239-257

Subject Terms: Finite difference methods applied to problems in solid mechanics, Boundary element methods for initial value and initial-boundary value problems involving PDEs, Vibrations in dynamical problems in solid mechanics, experiment, Finite difference methods for initial value and initial-boundary value problems involving PDEs, impact loading, narrow band random loading, ring stiffened cylindrical shell, Boundary element methods applied to problems in solid mechanics, vibro-acoustic response, boundary element method

File Description: application/xml

A Hybrid Collocation Method for Long‐Time Simulation of Heat Conduction in Anisotropic Functionally Graded Materials: A hybrid collocation method for long-time simulation of heat conduction in anisotropic functionally graded materials

Authors: Lin Qiu, Fajie Wang, Wenzhen Qu, Ji Lin, Yan Gu, Qing‐Hua Qin

Source: International Journal for Numerical Methods in Engineering. 126

Subject Terms: Iterative numerical methods for linear systems, anisotropic heat conduction, Numerical radial basis function approximation, Numerical computation of solutions to systems of equations, Diffusive and convective heat and mass transfer, heat flow, radial basis function collocation method, Finite difference methods applied to problems in solid mechanics, Computational methods for sparse matrices, Thermal effects in solid mechanics, Krylov deferred correction technique, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Spectral, collocation and related methods for boundary value problems involving PDEs, long-time simulation, PDEs in connection with mechanics of deformable solids, functionally graded materials, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

File Description: application/xml

Access URL: https://zbmath.org/7991422
https://doi.org/10.1002/nme.70002

A Generalized Single‐Step Multi‐Stage Time Integration Formulation and Novel Designs With Improved Stability and Accuracy: A generalized single-step multi-stage time integration formulation and novel designs with improved stability and accuracy

Authors: Yazhou Wang, Nikolaus A. Adams, Kumar K. Tamma

Source: International Journal for Numerical Methods in Engineering. 126

Subject Terms: Finite difference methods applied to problems in solid mechanics, RESEARCH ARTICLE, consistency analysis, local truncation error, multi-stage time integration algorithms, order reduction, structural dynamics, Numerical methods for initial value problems involving ordinary differential equations, ddc

File Description: application/xml; application/pdf

Access URL: https://mediatum.ub.tum.de/1780394

ANALYSIS OF THE DYNAMIC BEHAVIOR, BUCKLING, AND AEROELASTICITY OF A THIN COMPOSITE PLATE WITH THE EFFECT OF GENERAL AND LOCAL GEOMETRIC DEFECTS: Analysis of the dynamic behavior, buckling, and aeroelasticity of a thin composite plate with the effect of general and local geometric defects

Authors: Moosazadeh, H., Mohammadi, M. M.

Source: Journal of Applied Mechanics and Technical Physics. 65:134-151

Subject Terms: Finite difference methods applied to problems in solid mechanics, post-buckling, Runge-Kutta scheme, Thermal effects in solid mechanics, piston theory, flutter, thermal gradient, Composite and mixture properties, Galerkin weighted residual theory, Plates, Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.), Stability of dynamical problems in solid mechanics

File Description: application/xml

Access URL: https://zbmath.org/7968832
https://doi.org/10.1134/s0021894424010152

Implicit Relaxed All Mach Number Schemes for Gases and Compressible Materials: Implicit relaxed all Mach number schemes for gases and compressible materials

Authors: Thomann, Andrea, Iollo, Angelo, Puppo, Gabriella

Contributors: Iollo, Angelo

Source: SIAM Journal on Scientific Computing. 45:A2632-A2656

Subject Terms: Nonlinear elasticity, FOS: Physical sciences, Gas dynamics (general theory), [MATH] Mathematics [math], 01 natural sciences, Finite difference methods applied to problems in fluid mechanics, Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.), All-speed scheme, [PHYS] Physics [physics], Eulerian elasticity, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Finite volume methods for initial value and initial-boundary value problems involving PDEs, Finite volume methods applied to problems in solid mechanics, Finite difference methods for initial value and initial-boundary value problems involving PDEs, 0103 physical sciences, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, relaxation method, Finite volume methods for boundary value problems involving PDEs, Fluid Dynamics (physics.flu-dyn), Finite volume methods applied to problems in fluid mechanics, Physics - Fluid Dynamics, Numerical Analysis (math.NA), all-speed scheme, Euler equations, linearly implicit higher order methods, Finite difference methods applied to problems in solid mechanics, low Mach number limit, Numerical methods for stiff equations, Hyperbolic conservation laws, linearly implicit higher order schemes

File Description: application/xml; application/pdf

Access URL: http://arxiv.org/abs/2112.14126
https://zbmath.org/7749381
https://doi.org/10.1137/21m146819x
https://hal.science/hal-04375656v2
https://hal.science/hal-04375656v2/document
https://doi.org/10.1137/21m146819x
https://hdl.handle.net/11573/1706229
https://doi.org/10.1137/21M146819X

Stable and high-order accurate finite difference methods for the diffusive viscous wave equation

Authors: Siyang Wang

Source: Journal of Computational and Applied Mathematics. 463:116476

Subject Terms: Error estimate, acoustic wave, Beräkningsmatematik, Bulk waves in solid mechanics, seismic wave, error estimate, Numerical Analysis (math.NA), Finite difference methods applied to problems in solid mechanics, Computational Mathematics, numerical stability, Finite difference methods, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Summation by parts, summation-by-parts method, Mathematics - Numerical Analysis, discrete energy estimate, The diffusive viscous wave equation, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Stability, 65M06, 65M12

File Description: application/xml; application/pdf

Access URL: http://arxiv.org/abs/2501.05771
https://zbmath.org/8008549
https://doi.org/10.1016/j.cam.2024.116476
http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-234147

Radial migration and motion characteristics of elastic fibers in cylindrical Couette flow: a numerical simulation study

Authors: Cui, Jingyu, Liu, Yibo, Leng, Chunhui, Jin, Yuzhen

Source: Acta Mechanica. 234:6439-6450

Subject Terms: Incompressible viscous fluids, Finite difference methods applied to problems in solid mechanics, centrifugal force, fiber transport, Particle methods and lattice-gas methods, finite difference elastic solver, General theory of rotating fluids, immersed boundary-lattice Boltzmann fluid solver, Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.), rotating Couette flow

File Description: application/xml

Access URL: https://zbmath.org/7784016
https://doi.org/10.1007/s00707-023-03723-y

A symplectic finite element method based on Galerkin discretization for solving linear systems

Authors: Qiu, Zhiping, Wang, Zhao, Zhu, Bo

Source: Applied Mathematics and Mechanics. 44:1305-1316

Subject Terms: Finite difference methods applied to problems in solid mechanics, composite plate, Finite element methods applied to problems in solid mechanics, Vibrations in dynamical problems in solid mechanics, Classical linear elasticity, symplectic finite difference Runge-Kutta scheme, Bernoulli-Euler beam, Hamiltonian system, Birkhoffian system, Rods (beams, columns, shafts, arches, rings, etc.), vibration response, Plates, Galerkin finite element method

File Description: application/xml

Physics-informed deep learning for three-dimensional transient heat transfer analysis of functionally graded materials

Authors: Guo, Hongwei, Zhuang, Xiaoying, Fu, Xiaolong, Zhu, Yunzheng, Rabczuk, Timon

Source: Computational Mechanics. 72:513-524

Subject Terms: Functionally graded materials, Inhomogeneity in solid mechanics, Learning and adaptive systems in artificial intelligence, Deep learning, Physics-informed, 01 natural sciences, Activation function, Finite difference methods applied to problems in solid mechanics, Thermal effects in solid mechanics, Dewey Decimal Classification::000 | Allgemeines, Wissenschaft::000 | Informatik, Wissen, Systeme::004 | Informatik, Numerical and other methods in solid mechanics, Heat transfer, 0103 physical sciences, Discontinuous time scheme, activation function, Dewey Decimal Classification::500 | Naturwissenschaften::530 | Physik, 0101 mathematics, Runge-Kutta discrete time scheme, exponential material property variation

File Description: application/xml

Stability and Error Estimates of Gpav-Based Unconditionally Energy-Stable Scheme for Phase Field Crystal Equation: Stability and error estimates of GPAV-based unconditionally energy-stable scheme for phase field crystal equation

Authors: Yanxia Qian, Yongchao Zhang, Yunqing Huang

Source: Computers & Mathematics with Applications. 151:461-472

Subject Terms: positive, unconditional energy stability, Finite difference methods applied to problems in solid mechanics, Error bounds for initial value and initial-boundary value problems involving PDEs, error estimates, Spectral and related methods applied to problems in solid mechanics, Finite difference methods for initial value and initial-boundary value problems involving PDEs, phase field crystal, Nonlinear parabolic equations, Spectral, collocation and related methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, PDEs in connection with mechanics of deformable solids, Crystals in solids, auxiliary variable, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

File Description: application/xml

A combined mixed finite element method and discontinuous Galerkin method for hybrid-dimensional fracture models of two-phase flow

Authors: Chen, Shuangshuang

Source: Journal of Computational and Applied Mathematics. 459:116373

Subject Terms: Finite element methods applied to problems in solid mechanics, Flows in porous media, filtration, seepage, discontinuous Galerkin method, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, intersecting fractures, PDEs in connection with fluid mechanics, mixed finite element method, Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.), Finite difference methods applied to problems in fluid mechanics, Finite difference methods applied to problems in solid mechanics, two-phase flow, Error bounds for initial value and initial-boundary value problems involving PDEs, Brittle fracture, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Soil and rock mechanics, Liquid-liquid two component flows, hybrid-dimensional fracture model, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, PDEs in connection with mechanics of deformable solids, Finite element methods applied to problems in fluid mechanics

File Description: application/xml

Two-grid reduced-order method based on POD for a nonlinear poroelasticity model

Authors: Li, Hongpeng, Rui, Hongxing, Gao, Mengqi

Source: Journal of Computational and Applied Mathematics. 460:116413

Subject Terms: reduced-order finite element method, Linear elasticity with initial stresses, Finite element methods applied to problems in solid mechanics, nonlinear poroelasticity, Flows in porous media, filtration, seepage, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, PDEs in connection with fluid mechanics, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.), Finite difference methods applied to problems in fluid mechanics, Finite difference methods applied to problems in solid mechanics, Error bounds for initial value and initial-boundary value problems involving PDEs, proper orthogonal decomposition, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Soil and rock mechanics, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, two-grid method, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, PDEs in connection with mechanics of deformable solids, Finite element methods applied to problems in fluid mechanics

File Description: application/xml

Magneto-thermal-mechanical analysis of functionally graded thick-walled spherical vessels

Authors: Xie, Jun, Shi, Pengpeng, Li, Fengjun

Source: Acta Mechanica. 233:3405-3421

Subject Terms: Finite difference methods applied to problems in solid mechanics, analytical solution, Lorentz force effect, power-law material variation, Thermal effects in solid mechanics, 0203 mechanical engineering, Inhomogeneity in solid mechanics, Electromagnetic effects in solid mechanics, spherically symmetrical load, 02 engineering and technology, 0210 nano-technology, Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics, finite difference method

File Description: application/xml

A comparison of two nonconforming finite element methods for linear three-field poroelasticity

Authors: Guo, Jun, Shi, Yanchao, Luo, Weihua

Source: Demonstratio Mathematica, Vol 57, Iss 1, Pp 155-164 (2024)

Subject Terms: 65n30, Finite element methods applied to problems in solid mechanics, Flows in porous media, filtration, seepage, poroelasticity locking, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, PDEs in connection with fluid mechanics, Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.), locking-free, Finite difference methods applied to problems in solid mechanics, Sonstiges, Classical linear elasticity, nonconforming finite element method, Mathematik, Finite difference methods for initial value and initial-boundary value problems involving PDEs, QA1-939, biot's consolidation model, Biot's consolidation model, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, 74s05, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, PDEs in connection with mechanics of deformable solids, Geophysical solid mechanics, Mathematics

File Description: application/xml; image/jpeg; application/pdf

Access URL: https://zbmath.org/7976255
https://doi.org/10.1515/dema-2024-0073
https://doaj.org/article/1c58e4f2a1b2441a9bb3f1404b8392d6

Large-Amplitude Elastic Free-Surface Waves: Geometric Nonlinearity and Peakons: Large-amplitude elastic free-surface waves: geometric nonlinearity and peakons

Authors: Lawrence K. Forbes, Stephen J. Walters, Anya M. Reading

Source: Journal of Elasticity. 146:1-27

Subject Terms: peakons, Asymptotic behavior of solutions to PDEs, Surface waves in solid mechanics, FOS: Physical sciences, geometric nonlinearity, 02 engineering and technology, Condensed Matter - Soft Condensed Matter, surface waves, 01 natural sciences, Initial-boundary value problems for second-order hyperbolic systems, Geophysics (physics.geo-ph), Finite difference methods applied to problems in solid mechanics, Physics - Geophysics, 0203 mechanical engineering, numerical methods, Soft Condensed Matter (cond-mat.soft), curvature singularity, 0101 mathematics

File Description: application/xml

Access URL: http://arxiv.org/pdf/2108.07390
http://arxiv.org/abs/2108.07390
https://link.springer.com/article/10.1007/s10659-021-09852-6
https://arxiv.org/pdf/2108.07390
https://arxiv.org/abs/2108.07390
https://arxiv.org/pdf/2108.07390
http://ui.adsabs.harvard.edu/abs/2021arXiv210807390F/abstract

A reduced-dimension method for unknown Crank-Nicolson finite element solution coefficient vectors of elastic wave equation with singular source term

Authors: Luru Jing, Mingfu Feng, Yuejie Li, Fei Teng, Zhendong Luo

Source: Journal of Mathematical Analysis and Applications. 540:128629

Subject Terms: convergence, Linear elasticity with initial stresses, Finite element methods applied to problems in solid mechanics, existence, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, stability, elastic wave equation, Crank-Nicolson finite element method, Finite difference methods applied to problems in solid mechanics, Error bounds for initial value and initial-boundary value problems involving PDEs, proper orthogonal decomposition, reduced-dimension extrapolated Crank-Nicolson finite element method, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, PDEs in connection with mechanics of deformable solids

File Description: application/xml

A MGT thermoelastic problem with two relaxation parameters

Authors: Bazarra, Noelia, Fernández García, José Ramón, Quintanilla de Latorre, Ramón

Contributors: Universitat Politècnica de Catalunya. Departament de Matemàtiques

Source: Investigo. Repositorio Institucional de la Universidade de Vigo
Universidade de Vigo (UVigo)
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

Subject Terms: Finite element methods applied to problems in solid mechanics, finite element method, Finite elements, Classificació AMS::74 Mechanics of deformable solids::74F Coupling of solid mechanics with other effects, a priori error estimate, 1206 Análisis Numérico, exponential decay, 02 engineering and technology, 01 natural sciences, Classificació AMS::65 Numerical analysis::65M Partial differential equations, A priori error estimates, 0203 mechanical engineering, Exponential decay, initial value and time-dependent initial-boundary value problems, Classificació AMS::65 Numerical analysis::65M Partial differential equations, initial value and time-dependent initial-boundary value problems, 0101 mathematics, Thermoelasticity, MGT-thermoelasticity, foundations of continuum mechanics of solids, existence, Classificació AMS::74 Mechanics of deformable solids::74A Generalities, Uniqueness of solutions of dynamical problems in solid mechanics, uniqueness, implicit Euler scheme, linear semi-group theory, Finite difference methods applied to problems in solid mechanics, Thermal effects in solid mechanics, Existence of solutions of dynamical problems in solid mechanics, Classificació AMS::74 Mechanics of deformable solids::74A Generalities, axiomatics, foundations of continuum mechanics of solids, Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències, Linear semi-groups, PDEs in connection with mechanics of deformable solids, Relaxation parameters, Termoelasticitat, axiomatics

File Description: application/pdf; application/xml

Access URL: http://hdl.handle.net/11093/5279
https://link.springer.com/10.1007/s00033-023-02080-z
https://zbmath.org/7753767
https://doi.org/10.1007/s00033-023-02080-z
https://hdl.handle.net/2117/395197
https://doi.org/10.1007/s00033-023-02080-z

A meshless generalized finite difference method for 2D elasticity problems

Authors: Mas Irfan P. Hidayat, Rindang Fajarin, Widyastuti

Source: Engineering Analysis with Boundary Elements. 117:89-103

Subject Terms: Finite difference methods applied to problems in solid mechanics, B-spline shape function, 2D elasticity problems, generalized FD, Finite difference methods for initial value and initial-boundary value problems involving PDEs, 0103 physical sciences, triangle cells, 0101 mathematics, 01 natural sciences, meshless

File Description: application/xml

Access URL: https://zbmath.org/7228776
https://doi.org/10.1016/j.enganabound.2020.03.019
https://www.sciencedirect.com/science/article/pii/S0955799720300849