A fast multipole method(FMM)is applied for BEM to reduce both the operation and memory requirement in dealing with very large scale problems.In this paper,a new version of fast multipole BEM for 2D elastostatics is pr...A fast multipole method(FMM)is applied for BEM to reduce both the operation and memory requirement in dealing with very large scale problems.In this paper,a new version of fast multipole BEM for 2D elastostatics is presented and used for simulation of 2D elastic solid with a large number of randomly distributed inclusions combined with a similar subregion approach.Generalized minimum residual method(GMRES)is used as an iterative solver to solve the equation system formed by BEM iteratively.The numerical results show that the scheme presented is applicable to certain large scale problems.展开更多
The dynamical theories of elastic solids with microstructure are restudied and the reason why so many notations have been introduced for derivation of basic equations for such theories is given. In view of the existin...The dynamical theories of elastic solids with microstructure are restudied and the reason why so many notations have been introduced for derivation of basic equations for such theories is given. In view of the existing problems in those theories the rather general principle of power and energy rate is postulated and the equations of motion, the balance equations of energy rate and energy and the boundary conditions for local and nonlocal theories are naturally derived with help of that principle and the generalized Piola's theorem. These basic equations and the boundary conditions together with the initial conditions may be. used to solve the mixed problems of the dynamical theory of elastic solids with microstructure.展开更多
Two-dimensional stress wares in n general incompressible elastic solid are investigated. First, baxic equations for simple wares and shock waves are presented for a general strain energy junction. Then the characteris...Two-dimensional stress wares in n general incompressible elastic solid are investigated. First, baxic equations for simple wares and shock waves are presented for a general strain energy junction. Then the characteristic ware speeds and the associated characteristic vectors are deduced. It is shown that there usually exist two simple waves and two shock wares. Finally, two examples are given for the case of plane strain deformation and antiplane strain deformation, respectively. It is proved that, in the case of plane strain deformation, the oblique reflection problem of a plane shock is not solvable in general.展开更多
The generalized variational principles of isothermal quasi-static fluid full-filled elastic solids are established by using Variational Integral Method. Then by introducing constraints, several kinds of variational pr...The generalized variational principles of isothermal quasi-static fluid full-filled elastic solids are established by using Variational Integral Method. Then by introducing constraints, several kinds of variational principles are worked out, including five-field variable, four-field variable, three-field variable and two-field variable formulations. Some new variational principles are presented besides the principles noted in the previous works. Based on variational principles, finite element models can be set up.展开更多
In this work,in order to capture discontinuities correctly in linear elastic solid,augmented internal energy is defined according to the first law of thermodynamics and Hooke’s law.The non-conservative linear elastic...In this work,in order to capture discontinuities correctly in linear elastic solid,augmented internal energy is defined according to the first law of thermodynamics and Hooke’s law.The non-conservative linear elastic system is then rewritten into a conservative form with the help of an augmented total energy equation.We find that the non-physical oscillations occur to the popular HLL and HLLC approximate Riemann solvers when directly applied to simulate the augmented linear elastic solid.We analyze the intrinsic reason by defining a discrepancy factor which can be used to estimate the difference of the total stress across a contact discontinuity,where it is physically required to be continuous.We discover that non-physical oscillations inevitably appear in the vicinity of the contact discontinuity if this factor is away from zero for an approximate Riemann problem solver.In order to overcome this difficulty,we propose an approximate Riemann solver based on the linearized double-shock technique.Theoretical analysis and numerical results show that in comparison to the HLL and HLLC approximate Riemann solvers,the present linearized double-shock Riemann solver can eliminate the non-physical oscillations effectively.展开更多
Based on the new viewpoint of solid and gas interaction mechanics, gas leakage in a double deformable coal seam can be understood. That is, under the action of geophysical fields, the methane flow in a double deformab...Based on the new viewpoint of solid and gas interaction mechanics, gas leakage in a double deformable coal seam can be understood. That is, under the action of geophysical fields, the methane flow in a double deformable coal seam can be essentially considered to be compressible with time dependent and mixed permeation and diffusion through a pore cleat deformable heterogeneous and anisotropy medium. Based on this new viewpoint, a coupled mathematical model for coal seam deformation and gas leakage in a double coal seam was formulated and numerical simulations for gas emission from the coal seam are presented. It is found that coupled models might be closer to reality.展开更多
Based on the standard spaces of the physical presentation, both the quasi-static mechanical approximation and the quasi-static electromagnetic approximation of piezoelectric solids are studied here. The complete set o...Based on the standard spaces of the physical presentation, both the quasi-static mechanical approximation and the quasi-static electromagnetic approximation of piezoelectric solids are studied here. The complete set of uncoupled elastic wave and electromagnetic wave equations are deduced. The results show that the number and propagation speed of elastic waves and electromagnetic waves in anisotropic piezoelectric solids are determined by both the subspaces of electromagnetically anisotropic media and ones of mechanically anisotropic media. Based on these laws, we discuss the propagation behaviour of elastic waves and electromagnetic waves in the piezoelectric material of class 6 mm.展开更多
The elasticity,viz.,the deformation recoverability without energy dissipation,is known as a basic aspect in various deformation behaviors of solid materials.Typical examples are small and large elastic deformations ch...The elasticity,viz.,the deformation recoverability without energy dissipation,is known as a basic aspect in various deformation behaviors of solid materials.Typical examples are small and large elastic deformations characteristic of hard solids（e.g.,metals）and soft solids（e.g.,elastomers）,respectively.展开更多
Elastic wave scattering by a rough free surface of solids is analyzed. The analysis is based on the concept of scattering amplitude (SA) and perturbation approximation. The SA method is very convenient for rough surfa...Elastic wave scattering by a rough free surface of solids is analyzed. The analysis is based on the concept of scattering amplitude (SA) and perturbation approximation. The SA method is very convenient for rough surface scattering problems. By solving the boundary equations, the first and the second order solutions of approximate scattering amplitude are obtained. The general solutions are used for, as an example, the wave scattering by rough surfaces with Gaussian distribution. The mean field and variance are given. Finally, an experiment is designed to verify the theoretical predications.展开更多
基金The project supported by the National Nature Science Foundation of China(10172053)the Ministry of Education
文摘A fast multipole method(FMM)is applied for BEM to reduce both the operation and memory requirement in dealing with very large scale problems.In this paper,a new version of fast multipole BEM for 2D elastostatics is presented and used for simulation of 2D elastic solid with a large number of randomly distributed inclusions combined with a similar subregion approach.Generalized minimum residual method(GMRES)is used as an iterative solver to solve the equation system formed by BEM iteratively.The numerical results show that the scheme presented is applicable to certain large scale problems.
文摘The dynamical theories of elastic solids with microstructure are restudied and the reason why so many notations have been introduced for derivation of basic equations for such theories is given. In view of the existing problems in those theories the rather general principle of power and energy rate is postulated and the equations of motion, the balance equations of energy rate and energy and the boundary conditions for local and nonlocal theories are naturally derived with help of that principle and the generalized Piola's theorem. These basic equations and the boundary conditions together with the initial conditions may be. used to solve the mixed problems of the dynamical theory of elastic solids with microstructure.
文摘Two-dimensional stress wares in n general incompressible elastic solid are investigated. First, baxic equations for simple wares and shock waves are presented for a general strain energy junction. Then the characteristic ware speeds and the associated characteristic vectors are deduced. It is shown that there usually exist two simple waves and two shock wares. Finally, two examples are given for the case of plane strain deformation and antiplane strain deformation, respectively. It is proved that, in the case of plane strain deformation, the oblique reflection problem of a plane shock is not solvable in general.
文摘The generalized variational principles of isothermal quasi-static fluid full-filled elastic solids are established by using Variational Integral Method. Then by introducing constraints, several kinds of variational principles are worked out, including five-field variable, four-field variable, three-field variable and two-field variable formulations. Some new variational principles are presented besides the principles noted in the previous works. Based on variational principles, finite element models can be set up.
基金supported by the NSFC-NSAF joint fund(No.U1730118)the Post-doctoral Science Foundation of China(No.2020M680283)the Science Challenge Project(No.JCKY2016212A502).
文摘In this work,in order to capture discontinuities correctly in linear elastic solid,augmented internal energy is defined according to the first law of thermodynamics and Hooke’s law.The non-conservative linear elastic system is then rewritten into a conservative form with the help of an augmented total energy equation.We find that the non-physical oscillations occur to the popular HLL and HLLC approximate Riemann solvers when directly applied to simulate the augmented linear elastic solid.We analyze the intrinsic reason by defining a discrepancy factor which can be used to estimate the difference of the total stress across a contact discontinuity,where it is physically required to be continuous.We discover that non-physical oscillations inevitably appear in the vicinity of the contact discontinuity if this factor is away from zero for an approximate Riemann problem solver.In order to overcome this difficulty,we propose an approximate Riemann solver based on the linearized double-shock technique.Theoretical analysis and numerical results show that in comparison to the HLL and HLLC approximate Riemann solvers,the present linearized double-shock Riemann solver can eliminate the non-physical oscillations effectively.
文摘Based on the new viewpoint of solid and gas interaction mechanics, gas leakage in a double deformable coal seam can be understood. That is, under the action of geophysical fields, the methane flow in a double deformable coal seam can be essentially considered to be compressible with time dependent and mixed permeation and diffusion through a pore cleat deformable heterogeneous and anisotropy medium. Based on this new viewpoint, a coupled mathematical model for coal seam deformation and gas leakage in a double coal seam was formulated and numerical simulations for gas emission from the coal seam are presented. It is found that coupled models might be closer to reality.
文摘Based on the standard spaces of the physical presentation, both the quasi-static mechanical approximation and the quasi-static electromagnetic approximation of piezoelectric solids are studied here. The complete set of uncoupled elastic wave and electromagnetic wave equations are deduced. The results show that the number and propagation speed of elastic waves and electromagnetic waves in anisotropic piezoelectric solids are determined by both the subspaces of electromagnetically anisotropic media and ones of mechanically anisotropic media. Based on these laws, we discuss the propagation behaviour of elastic waves and electromagnetic waves in the piezoelectric material of class 6 mm.
文摘The elasticity,viz.,the deformation recoverability without energy dissipation,is known as a basic aspect in various deformation behaviors of solid materials.Typical examples are small and large elastic deformations characteristic of hard solids（e.g.,metals）and soft solids（e.g.,elastomers）,respectively.
基金This work was supported by the National Natural Science Foundation of China(19774062).
文摘Elastic wave scattering by a rough free surface of solids is analyzed. The analysis is based on the concept of scattering amplitude (SA) and perturbation approximation. The SA method is very convenient for rough surface scattering problems. By solving the boundary equations, the first and the second order solutions of approximate scattering amplitude are obtained. The general solutions are used for, as an example, the wave scattering by rough surfaces with Gaussian distribution. The mean field and variance are given. Finally, an experiment is designed to verify the theoretical predications.
