An adaptive cell-based domain integration method（CDIM） is proposed for the treatment of domain integrals in 3D boundary element method（BEM）. The domain integrals are computed in background cells rather than volume...An adaptive cell-based domain integration method（CDIM） is proposed for the treatment of domain integrals in 3D boundary element method（BEM）. The domain integrals are computed in background cells rather than volume elements. The cells are created from the boundary elements based on an adaptive oct-tree structure and no other discretization is needed. Cells containing the boundary elements are subdivided into smaller sub-cells adaptively according to the sizes and levels of the boundary elements; and the sub-cells outside the domain are deleted to obtain the desired accuracy. The method is applied in the 3D potential and elasticity problems in this paper.展开更多
The symplectic approach proposed and developed by Zhong et al. in 1990s for elasticity problems is a rational analytical method, in which ample experience is not needed as in the conventional semi-inverse method. In t...The symplectic approach proposed and developed by Zhong et al. in 1990s for elasticity problems is a rational analytical method, in which ample experience is not needed as in the conventional semi-inverse method. In the symplectic space, elasticity problems can be solved using the method of separation of variables along with the eigenfunction expansion technique, as in traditional Fourier analysis. The eigensolutions include those corresponding to zero and nonzero eigenvalues. The latter group can be further divided into α-and β-sets. This paper reformulates the form of β-set eigensolutions to achieve the stability of numerical calculation, which is very important to obtain accurate results within the symplectic frame. An example is finally given and numerical results are compared and discussed.展开更多
An analytical scheme, which avoids using the standard Gaussian approximate quadrature to treat the boundary integrals in direct boundary element method (DBEM) of two-dimensional potential and elastic problems, is esta...An analytical scheme, which avoids using the standard Gaussian approximate quadrature to treat the boundary integrals in direct boundary element method (DBEM) of two-dimensional potential and elastic problems, is established. With some numerical results, it is shown that the better precision and high computational efficiency, especially in the band of the domain near boundary, can be derived by the present scheme.展开更多
The singular boundary method （SBM） is a recent meshless boundary collocation method that remedies the perplexing drawback of fictitious boundary in the method of fundamental solutions （MFS）. The basic idea is to u...The singular boundary method （SBM） is a recent meshless boundary collocation method that remedies the perplexing drawback of fictitious boundary in the method of fundamental solutions （MFS）. The basic idea is to use the origin intensity factor to eliminate singularity of the fundamental solution at source. The method has so far been applied successfully to the potential and elasticity problems. However, the SBM solution for large-scale problems has been hindered by the operation count of O（N^3） with direct solvers or O（N^2） with iterative solvers, as well as the memory requirement of O（N^2）. In this study, the first attempt was made to combine the fast multipole method （FMM） and the SBM to significantly reduce CPU time and memory requirement by one degree of magnitude, namely, O（N）. Based on the complex variable represen- tation of fundamental solutions, the FMM-SBM formulations for both displacement and traction were presented. Numerical examples with up to hundreds of thousands of unknowns have successfully been tested on a desktop computer. These results clearly illustrated that the proposed FMM-SBM was very efficient and promising in solving large-scale plane elasticity problems.展开更多
In the use of finite element methods to the planar elasticity problems,one diffculty is to overcome locking when elasticity constant λ→∞.In the case of traction boundary condition,another diffculty is to make the d...In the use of finite element methods to the planar elasticity problems,one diffculty is to overcome locking when elasticity constant λ→∞.In the case of traction boundary condition,another diffculty is to make the discrete Korn＇s second inequality valid.In this paper,a triangular element is presented.We prove that this element is locking-free,the discrete Korn＇s second inequality holds and the convergence order is two.展开更多
Without applying any stable element techniques in the mixed methods, two simple generalized mixed element(GME) formulations were derived by combining the minimum potential energy principle and Hellinger–Reissner(H–R...Without applying any stable element techniques in the mixed methods, two simple generalized mixed element(GME) formulations were derived by combining the minimum potential energy principle and Hellinger–Reissner(H–R) variational principle. The main features of the GME formulations are that the common C0-continuous polynomial shape functions for displacement methods are used to express both displacement and stress variables, and the coefficient matrix of these formulations is not only automatically symmetric but also invertible. Hence, the numerical results of the generalized mixed methods based on the GME formulations are stable. Displacement as well as stress results can be obtained directly from the algebraic system for finite element analysis after introducing stress and displacement boundary conditions simultaneously. Numerical examples show that displacement and stress results retain the same accuracy. The results of the noncompatible generalized mixed method proposed herein are more accurate than those of the standard noncompatible displacement method. The noncompatible generalized mixed element is less sensitive to element geometric distortions.展开更多
In the present paper, the spectrums of off-diagonal infinite-dimensional Hamiltonian operators are studied. At first, we prove that the spectrum, the continuous-spectrum, and the union of the point-spectrum and residu...In the present paper, the spectrums of off-diagonal infinite-dimensional Hamiltonian operators are studied. At first, we prove that the spectrum, the continuous-spectrum, and the union of the point-spectrum and residual- spectrum of the operators are symmetric with respect to real axis and imaginary axis. Then for the purpose of reducing the dimension of the studied problems, the spectrums of the operators are expressed by the spectrums of the product of two self-adjoint operators in state spac,3. At last, the above-mentioned results are applied to plane elasticity problems, which shows the practicability of the results.展开更多
This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial diffe...This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method.展开更多
This paper introduces an adaptive finite element method （AFEM） using the newest vertex bisection and marking exclusively according to the error estimator without special treatment of oscillation. By the combination ...This paper introduces an adaptive finite element method （AFEM） using the newest vertex bisection and marking exclusively according to the error estimator without special treatment of oscillation. By the combination of the global lower bound and the localized upper bound of the posteriori error estimator, perturbation of oscillation, and cardinality of the marked element set, it is proved that the AFEM is quasi-optimal for linear elasticity problems in two dimensions, and this conclusion is verified by the numerical examples.展开更多
In this paper, the author obtains the more general displacement solutions for the isotropic plane elasticity problems. The general solution obtained in ref. [ 1 ] is merely the particular case of this paper, In compar...In this paper, the author obtains the more general displacement solutions for the isotropic plane elasticity problems. The general solution obtained in ref. [ 1 ] is merely the particular case of this paper, In comparison with ref. [1], the general solutions of this paper contain more arbitrary constants. Thus they may satisfy more boundary conditions.展开更多
This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problem...This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper tri angular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler com plete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and conve nient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example.展开更多
A localized version of the method of fundamental solution(LMFS)is devised in this paper for the numerical solutions of three-dimensional(3D)elasticity problems.The present method combines the advantages of high comput...A localized version of the method of fundamental solution(LMFS)is devised in this paper for the numerical solutions of three-dimensional(3D)elasticity problems.The present method combines the advantages of high computational efficiency of localized discretization schemes and the pseudo-spectral convergence rate of the classical MFS formulation.Such a combination will be an important improvement to the classical MFS for complicated and large-scale engineering simulations.Numerical examples with up to 100,000 unknowns can be solved without any difficulty on a personal computer using the developed methodologies.The advantages,disadvantages and potential applications of the proposed method,as compared with the classical MFS and boundary element method(BEM),are discussed.展开更多
Here,we describe the robust and efficient application of the conventional 3D BEM in solving elasticity problems. We have focused on the precise computation of weakly singular integrals. The conformal Duffy-distance tr...Here,we describe the robust and efficient application of the conventional 3D BEM in solving elasticity problems. We have focused on the precise computation of weakly singular integrals. The conformal Duffy-distance transformation was employed to alleviate near singularities caused from two aspects:(1) the large aspect ratio of elements,i.e.,element shape distortions;and(2)the closeness of element boundaries to field points,i.e.,ill-shaped patches. Then,the rigid body motion method was employed to evaluate strongly singular integrals. Numerical solutions of 3D elastostatic problems demonstrated the high accuracy of the proposed method with coarse meshes and high convergence rates with mesh refinement. Compared with the Duffy transformation and original polar coordinate transformations,the proposed method is insensitive to element shapes.展开更多
A posteriori error estimators for the symmetric mixed finite element methods for linear elasticity problems with Dirichlet and mixed boundary conditions are proposed. Reliability and efficiency of the estimators are p...A posteriori error estimators for the symmetric mixed finite element methods for linear elasticity problems with Dirichlet and mixed boundary conditions are proposed. Reliability and efficiency of the estimators are proved. Numerical examples are presented to verify the theoretical results.展开更多
In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body...In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body-fitted meshes are used.For homogeneous jump conditions,both non-conforming and conforming basis functions are constructed in such a way that they satisfy the natural jump conditions. For non-homogeneous jump conditions,a pair of functions that satisfy the same non-homogeneous jump conditions are constructed using a level-set representation of the interface.With such a pair of functions,the discontinuities across the interface in the solution and flux are removed;and an equivalent elasticity interface problem with homogeneous jump conditions is formulated.Numerical examples are presented to demonstrate that such methods have second order convergence.展开更多
In this paper, a locking-free nonconforming rectangular finite element scheme is presented for the planar elasticity problem with pure displacement boundary condition. Meanwhile, we prove that this element is also con...In this paper, a locking-free nonconforming rectangular finite element scheme is presented for the planar elasticity problem with pure displacement boundary condition. Meanwhile, we prove that this element is also convergent for stationary Stokes problem.展开更多
As suggested by the title, this extensive book is concerned with crack and contact prob- lems in linear elasticity. However, in general, it is intended for a wide audience ranging from engineers to mathematical physic...As suggested by the title, this extensive book is concerned with crack and contact prob- lems in linear elasticity. However, in general, it is intended for a wide audience ranging from engineers to mathematical physicists. Indeed, numerous problems of both academic and tech- nological interest in electro-magnetics, acoustics, solid and fluid dynamics, etc. are actually related to each other and governed by the same mixed boundary value problems from a unified mathematical standpoint展开更多
In this paper, some thermoelastic problems in the half space are studied by using the general solutions of the elastic equations. The method presented here is extremely effective for the axisymmetric problems of the h...In this paper, some thermoelastic problems in the half space are studied by using the general solutions of the elastic equations. The method presented here is extremely effective for the axisymmetric problems of the half space as well as the half plane problems.展开更多
In this paper the method of reciprocal theorem is extended to find solutions of plane problems of elasticity of the rectangular plates with various edge conditions.First we give the basic solution of the plane problem...In this paper the method of reciprocal theorem is extended to find solutions of plane problems of elasticity of the rectangular plates with various edge conditions.First we give the basic solution of the plane problem of the rectangular plate with four edges built-in as the basic system and then find displacement expressions of the actual system by using the reciprocal theorem between the basic system and actual system with various edge conditions.When only displacement edge conditions exist, obtaining displacement expressions by means of the method of reciprocal theorem is actual. But in other conditions, when static force edge conditions or mixed ones exist, the obtained displacements are admissible. In order to find actual displacement, the minimum potential energy theorem must be applied.Calculations show that the method of reciprocal theorem is a simple, convenient and general one for the solution of plane problems of elasticity of the rectangular plates with various edge conditions. Evidently, it is a new method.展开更多
The fracture theory of cubic quasicrystal was developed. The exact analytic solution of a Mode Ⅲ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, and so t...The fracture theory of cubic quasicrystal was developed. The exact analytic solution of a Mode Ⅲ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, and so the displacement and stress fields, the stress intensity factor and strain energy release rate were determined. The results show that the stress intensity factor is independent of material constants, and the strain energy release rate is dependent on all material constants. These provide important information for studying the deformation and fracture of the new solid material.展开更多
基金Financial support for the project from the National Natural Science Foundation of China(No.51609181)
文摘An adaptive cell-based domain integration method（CDIM） is proposed for the treatment of domain integrals in 3D boundary element method（BEM）. The domain integrals are computed in background cells rather than volume elements. The cells are created from the boundary elements based on an adaptive oct-tree structure and no other discretization is needed. Cells containing the boundary elements are subdivided into smaller sub-cells adaptively according to the sizes and levels of the boundary elements; and the sub-cells outside the domain are deleted to obtain the desired accuracy. The method is applied in the 3D potential and elasticity problems in this paper.
基金the National Natural Science Foundation of China (Nos. 10725210 and 10432030) the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20060335107)the Program for New Century Excellent Talents in University, MOE, China (No. NCET-05-05010)
文摘The symplectic approach proposed and developed by Zhong et al. in 1990s for elasticity problems is a rational analytical method, in which ample experience is not needed as in the conventional semi-inverse method. In the symplectic space, elasticity problems can be solved using the method of separation of variables along with the eigenfunction expansion technique, as in traditional Fourier analysis. The eigensolutions include those corresponding to zero and nonzero eigenvalues. The latter group can be further divided into α-and β-sets. This paper reformulates the form of β-set eigensolutions to achieve the stability of numerical calculation, which is very important to obtain accurate results within the symplectic frame. An example is finally given and numerical results are compared and discussed.
文摘An analytical scheme, which avoids using the standard Gaussian approximate quadrature to treat the boundary integrals in direct boundary element method (DBEM) of two-dimensional potential and elastic problems, is established. With some numerical results, it is shown that the better precision and high computational efficiency, especially in the band of the domain near boundary, can be derived by the present scheme.
基金Project supported by the National Basic Research Program of China(973 ProjectNo.2010CB832702)+4 种基金the National Science Funds for Distinguished Young Scholars of China(No.11125208)the National Natural Science Foundation of China(Nos.11125208 and 11302069)the 111 project under Grant B12032Jiangsu Province Graduate Students Research and Innovation Plan(No.KYZZ 0138)the scholarship from the China Scholarship Council(CSC)(No.201306710026)
文摘The singular boundary method （SBM） is a recent meshless boundary collocation method that remedies the perplexing drawback of fictitious boundary in the method of fundamental solutions （MFS）. The basic idea is to use the origin intensity factor to eliminate singularity of the fundamental solution at source. The method has so far been applied successfully to the potential and elasticity problems. However, the SBM solution for large-scale problems has been hindered by the operation count of O（N^3） with direct solvers or O（N^2） with iterative solvers, as well as the memory requirement of O（N^2）. In this study, the first attempt was made to combine the fast multipole method （FMM） and the SBM to significantly reduce CPU time and memory requirement by one degree of magnitude, namely, O（N）. Based on the complex variable represen- tation of fundamental solutions, the FMM-SBM formulations for both displacement and traction were presented. Numerical examples with up to hundreds of thousands of unknowns have successfully been tested on a desktop computer. These results clearly illustrated that the proposed FMM-SBM was very efficient and promising in solving large-scale plane elasticity problems.
文摘In the use of finite element methods to the planar elasticity problems,one diffculty is to overcome locking when elasticity constant λ→∞.In the case of traction boundary condition,another diffculty is to make the discrete Korn＇s second inequality valid.In this paper,a triangular element is presented.We prove that this element is locking-free,the discrete Korn＇s second inequality holds and the convergence order is two.
基金supported by the National Natural Science Foundation of China (Grant 11502286)
文摘Without applying any stable element techniques in the mixed methods, two simple generalized mixed element(GME) formulations were derived by combining the minimum potential energy principle and Hellinger–Reissner(H–R) variational principle. The main features of the GME formulations are that the common C0-continuous polynomial shape functions for displacement methods are used to express both displacement and stress variables, and the coefficient matrix of these formulations is not only automatically symmetric but also invertible. Hence, the numerical results of the generalized mixed methods based on the GME formulations are stable. Displacement as well as stress results can be obtained directly from the algebraic system for finite element analysis after introducing stress and displacement boundary conditions simultaneously. Numerical examples show that displacement and stress results retain the same accuracy. The results of the noncompatible generalized mixed method proposed herein are more accurate than those of the standard noncompatible displacement method. The noncompatible generalized mixed element is less sensitive to element geometric distortions.
基金supported by the National Natural Science Foundation of China under Grant No.10562002the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No.20070126002+1 种基金the Natural Science Foundation of Inner Mongolia under Grant No.200508010103the Inner Mongolia University Scientific Research Starting Foundation for Talented Scholars under Grant No.207066
文摘In the present paper, the spectrums of off-diagonal infinite-dimensional Hamiltonian operators are studied. At first, we prove that the spectrum, the continuous-spectrum, and the union of the point-spectrum and residual- spectrum of the operators are symmetric with respect to real axis and imaginary axis. Then for the purpose of reducing the dimension of the studied problems, the spectrums of the operators are expressed by the spectrums of the product of two self-adjoint operators in state spac,3. At last, the above-mentioned results are applied to plane elasticity problems, which shows the practicability of the results.
基金Project supported by the National Natural Science Foundation of China (No. 10962004)the Special-ized Research Fund for the Doctoral Program of Higher Education of China (No. 20070126002)+1 种基金the Chunhui Program of Ministry of Education of China (No. Z2009-1-01010)the Natural Science Foundation of Inner Mongolia (No. 2009BS0101)
文摘This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method.
基金Project supported by the National Natural Science Foundation of China(Nos.1120115911426102+4 种基金and 11571293)the Natural Science Foundation of Hunan Province(No.11JJ3135)the Foundation for Outstanding Young Teachers in Higher Education of Guangdong Province(No.Yq2013054)the Pearl River S&T Nova Program of Guangzhou(No.2013J2200063)the Construct Program of the Key Discipline in Hunan University of Science and Engineering
文摘This paper introduces an adaptive finite element method （AFEM） using the newest vertex bisection and marking exclusively according to the error estimator without special treatment of oscillation. By the combination of the global lower bound and the localized upper bound of the posteriori error estimator, perturbation of oscillation, and cardinality of the marked element set, it is proved that the AFEM is quasi-optimal for linear elasticity problems in two dimensions, and this conclusion is verified by the numerical examples.
文摘In this paper, the author obtains the more general displacement solutions for the isotropic plane elasticity problems. The general solution obtained in ref. [ 1 ] is merely the particular case of this paper, In comparison with ref. [1], the general solutions of this paper contain more arbitrary constants. Thus they may satisfy more boundary conditions.
基金supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20070126002)the National Natural Science Foundation of China (No. 10962004)
文摘This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper tri angular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler com plete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and conve nient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example.
基金supported by the National Natural Science Foundation of China(Nos.11872220,11772119)the Natural Science Foundation of Shandong Province of China(Nos.ZR2017JL004,2019KJI009)。
文摘A localized version of the method of fundamental solution(LMFS)is devised in this paper for the numerical solutions of three-dimensional(3D)elasticity problems.The present method combines the advantages of high computational efficiency of localized discretization schemes and the pseudo-spectral convergence rate of the classical MFS formulation.Such a combination will be an important improvement to the classical MFS for complicated and large-scale engineering simulations.Numerical examples with up to 100,000 unknowns can be solved without any difficulty on a personal computer using the developed methodologies.The advantages,disadvantages and potential applications of the proposed method,as compared with the classical MFS and boundary element method(BEM),are discussed.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.51879245,41731284&11672360)the Fundamental Research Funds for the Central Universities,China University of Geosciences(Wuhan)(Grant Nos.CUGCJ1821&CUG170645)。
文摘Here,we describe the robust and efficient application of the conventional 3D BEM in solving elasticity problems. We have focused on the precise computation of weakly singular integrals. The conformal Duffy-distance transformation was employed to alleviate near singularities caused from two aspects:(1) the large aspect ratio of elements,i.e.,element shape distortions;and(2)the closeness of element boundaries to field points,i.e.,ill-shaped patches. Then,the rigid body motion method was employed to evaluate strongly singular integrals. Numerical solutions of 3D elastostatic problems demonstrated the high accuracy of the proposed method with coarse meshes and high convergence rates with mesh refinement. Compared with the Duffy transformation and original polar coordinate transformations,the proposed method is insensitive to element shapes.
基金supported by National Science Foundation of USA(Grant No.DMS-1418934)the Sea Poly Project of Beijing Overseas Talents,National Natural Science Foundation of China(Grant Nos.11625101,91430213,11421101,11771338,11671304 and 11401026)+1 种基金Zhejiang Provincial Natural Science Foundation of China Projects(Grant Nos.LY17A010010,LY15A010015 and LY15A010016)Wenzhou Science and Technology Plan Project(Grant No.G20160019)
文摘A posteriori error estimators for the symmetric mixed finite element methods for linear elasticity problems with Dirichlet and mixed boundary conditions are proposed. Reliability and efficiency of the estimators are proved. Numerical examples are presented to verify the theoretical results.
基金supported by the US ARO grants 49308-MA and 56349-MAthe US AFSOR grant FA9550-06-1-024+1 种基金he US NSF grant DMS-0911434the State Key Laboratory of Scientific and Engineering Computing of Chinese Academy of Sciences during a visit by Z.Li between July-August,2008.
文摘In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body-fitted meshes are used.For homogeneous jump conditions,both non-conforming and conforming basis functions are constructed in such a way that they satisfy the natural jump conditions. For non-homogeneous jump conditions,a pair of functions that satisfy the same non-homogeneous jump conditions are constructed using a level-set representation of the interface.With such a pair of functions,the discontinuities across the interface in the solution and flux are removed;and an equivalent elasticity interface problem with homogeneous jump conditions is formulated.Numerical examples are presented to demonstrate that such methods have second order convergence.
文摘In this paper, a locking-free nonconforming rectangular finite element scheme is presented for the planar elasticity problem with pure displacement boundary condition. Meanwhile, we prove that this element is also convergent for stationary Stokes problem.
文摘As suggested by the title, this extensive book is concerned with crack and contact prob- lems in linear elasticity. However, in general, it is intended for a wide audience ranging from engineers to mathematical physicists. Indeed, numerous problems of both academic and tech- nological interest in electro-magnetics, acoustics, solid and fluid dynamics, etc. are actually related to each other and governed by the same mixed boundary value problems from a unified mathematical standpoint
文摘In this paper, some thermoelastic problems in the half space are studied by using the general solutions of the elastic equations. The method presented here is extremely effective for the axisymmetric problems of the half space as well as the half plane problems.
文摘In this paper the method of reciprocal theorem is extended to find solutions of plane problems of elasticity of the rectangular plates with various edge conditions.First we give the basic solution of the plane problem of the rectangular plate with four edges built-in as the basic system and then find displacement expressions of the actual system by using the reciprocal theorem between the basic system and actual system with various edge conditions.When only displacement edge conditions exist, obtaining displacement expressions by means of the method of reciprocal theorem is actual. But in other conditions, when static force edge conditions or mixed ones exist, the obtained displacements are admissible. In order to find actual displacement, the minimum potential energy theorem must be applied.Calculations show that the method of reciprocal theorem is a simple, convenient and general one for the solution of plane problems of elasticity of the rectangular plates with various edge conditions. Evidently, it is a new method.
文摘The fracture theory of cubic quasicrystal was developed. The exact analytic solution of a Mode Ⅲ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, and so the displacement and stress fields, the stress intensity factor and strain energy release rate were determined. The results show that the stress intensity factor is independent of material constants, and the strain energy release rate is dependent on all material constants. These provide important information for studying the deformation and fracture of the new solid material.
