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Alberto Salvadori - One of the best experts on this subject based on the ideXlab platform.
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transient analysis of the dynamic stress intensity factors using sgbem for frequency domain elastodynamics
Computer Methods in Applied Mechanics and Engineering, 2010Co-Authors: A V Phan, L J Gray, Alberto SalvadoriAbstract:In this paper, a two-dimensional symmetric-Galerkin boundary integral formulation for elastodynamic fracture analysis in the frequency domain is described. The numerical implementation is carried out with quadratic elements, allowing the use of an improved quarter-point element for accurately determining frequency responses of the dynamic stress intensity factors (DSIFs). To deal with singular and hypersingular integrals, the formulation is decomposed into two parts: the first part is identical to that for Elastostatics while the second part contains at most logarithmic singularities. The treatment of the elastostatic singular and hypersingular singular integrals employs an exterior limit to the boundary, while the weakly singular integrals in the second part are handled by Gauss quadrature. Time histories (transient responses) of the DSIFs can be obtained in a post-processing step by applying the standard fast Fourier transform (FFT) and algorithm to the frequency responses of these DSIFs. Several test examples are presented for the calculation of the DSIFs due to two types of impact loading: Heaviside step loading and blast loading. The results suggest that the combination of the symmetric-Galerkin boundary element method and standard FFT algorithms in determining transient responses of the DSIFs is a robust and effective technique.
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symmetric galerkin boundary element analysis of the dynamic stress intensity factors in the frequency domain
Mechanics Research Communications, 2010Co-Authors: A V Phan, L J Gray, Alberto SalvadoriAbstract:A two-dimensional symmetric-Galerkin boundary integral formulation for the analysis of the dynamic stress intensity factors (DSIFs) in the frequency domain is described. A quadratic element is employed, allowing the use of the modified quarter-point element at the crack tip. For singular and hypersingular integrals, this formulation is decomposed into two parts: the first part is identical to those for Elastostatics while the second part, at most, contains only logarithmic singularities. The treatment of the elastostatic singular and hypersingular integrals is carried out by means of an exterior limit to the boundary, while the weakly singular integrals in the second part are handled by Gauss quadrature. Test examples are presented for the calculation of the DSIFs due to harmonic loading as well as wave scattering from a crack.
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Symmetric-Galerkin Boundary Element Transient Analysis of the DSIFs for the Interaction of a Crack with a Circular Inclusion
Key Engineering Materials, 2010Co-Authors: A V Phan, L J Gray, Alberto SalvadoriAbstract:A dynamic analysis of crack-inclusion interaction is described in this paper. The analysis employs a two-dimensional symmetric-Galerkin boundary integral formulation for multi-domain elastodynamic fracture analysis in the frequency domain. The multi-domain technique is based on the assumption of perfectly bonded inclusions. The numerical implementation of this boundary integral formulation is carried out with standard quadratic elements, allowing the use of an improved quarter-point element for accurately determining frequency responses of the dynamic stress intensity factors (DSIFs). To deal with singular and hypersingular integrals, the formulation is decomposed into two parts: the rst part is identical to that for Elastostatics while the second part contains at most logarithmic singularities. The treatment of the elastostatic singular and hypersingular singular integrals employs an exterior limit to the boundary, while the weakly singular integrals in the second part are handled by Gauss quadrature. Time histories (transient responses) of the DSIFs are obtained in a post-processing step by applying the fast Fourier transform (FFT) and inverse FFT to the frequency responses of these DSIFs. Two numerical examples are presented for the computation of the DSIFs due to crack-inclusion interaction under two types of impact loading: Heaviside step loading and blast loading. The numerical results are consistent and con rm the well known crack tip shielding mechanism observed during the interaction between a crack and a much sti er inclusion.
A V Phan - One of the best experts on this subject based on the ideXlab platform.
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transient analysis of the dynamic stress intensity factors using sgbem for frequency domain elastodynamics
Computer Methods in Applied Mechanics and Engineering, 2010Co-Authors: A V Phan, L J Gray, Alberto SalvadoriAbstract:In this paper, a two-dimensional symmetric-Galerkin boundary integral formulation for elastodynamic fracture analysis in the frequency domain is described. The numerical implementation is carried out with quadratic elements, allowing the use of an improved quarter-point element for accurately determining frequency responses of the dynamic stress intensity factors (DSIFs). To deal with singular and hypersingular integrals, the formulation is decomposed into two parts: the first part is identical to that for Elastostatics while the second part contains at most logarithmic singularities. The treatment of the elastostatic singular and hypersingular singular integrals employs an exterior limit to the boundary, while the weakly singular integrals in the second part are handled by Gauss quadrature. Time histories (transient responses) of the DSIFs can be obtained in a post-processing step by applying the standard fast Fourier transform (FFT) and algorithm to the frequency responses of these DSIFs. Several test examples are presented for the calculation of the DSIFs due to two types of impact loading: Heaviside step loading and blast loading. The results suggest that the combination of the symmetric-Galerkin boundary element method and standard FFT algorithms in determining transient responses of the DSIFs is a robust and effective technique.
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symmetric galerkin boundary element analysis of the dynamic stress intensity factors in the frequency domain
Mechanics Research Communications, 2010Co-Authors: A V Phan, L J Gray, Alberto SalvadoriAbstract:A two-dimensional symmetric-Galerkin boundary integral formulation for the analysis of the dynamic stress intensity factors (DSIFs) in the frequency domain is described. A quadratic element is employed, allowing the use of the modified quarter-point element at the crack tip. For singular and hypersingular integrals, this formulation is decomposed into two parts: the first part is identical to those for Elastostatics while the second part, at most, contains only logarithmic singularities. The treatment of the elastostatic singular and hypersingular integrals is carried out by means of an exterior limit to the boundary, while the weakly singular integrals in the second part are handled by Gauss quadrature. Test examples are presented for the calculation of the DSIFs due to harmonic loading as well as wave scattering from a crack.
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Symmetric-Galerkin Boundary Element Transient Analysis of the DSIFs for the Interaction of a Crack with a Circular Inclusion
Key Engineering Materials, 2010Co-Authors: A V Phan, L J Gray, Alberto SalvadoriAbstract:A dynamic analysis of crack-inclusion interaction is described in this paper. The analysis employs a two-dimensional symmetric-Galerkin boundary integral formulation for multi-domain elastodynamic fracture analysis in the frequency domain. The multi-domain technique is based on the assumption of perfectly bonded inclusions. The numerical implementation of this boundary integral formulation is carried out with standard quadratic elements, allowing the use of an improved quarter-point element for accurately determining frequency responses of the dynamic stress intensity factors (DSIFs). To deal with singular and hypersingular integrals, the formulation is decomposed into two parts: the rst part is identical to that for Elastostatics while the second part contains at most logarithmic singularities. The treatment of the elastostatic singular and hypersingular singular integrals employs an exterior limit to the boundary, while the weakly singular integrals in the second part are handled by Gauss quadrature. Time histories (transient responses) of the DSIFs are obtained in a post-processing step by applying the fast Fourier transform (FFT) and inverse FFT to the frequency responses of these DSIFs. Two numerical examples are presented for the computation of the DSIFs due to crack-inclusion interaction under two types of impact loading: Heaviside step loading and blast loading. The numerical results are consistent and con rm the well known crack tip shielding mechanism observed during the interaction between a crack and a much sti er inclusion.
Ming-gong Lee - One of the best experts on this subject based on the ideXlab platform.
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Error analysis of the method of fundamental solutions for linear Elastostatics
Journal of Computational and Applied Mathematics, 2013Co-Authors: Hung-tsai Huang, Ming-gong Lee, John Y. ChiangAbstract:For linear Elastostatics in 2D, the Trefftz methods (i.e., the boundary methods) using the particular solutions and the fundamental solutions satisfying the Cauchy-Navier equation lead to the method of particular solutions (MPS) and the method of fundamental solutions (MFS), respectively. In this paper, the mixed types of the displacement and the traction boundary conditions are dealt with, and both the direct collocation techniques and the Lagrange multiplier are used to couple the boundary conditions. The former is just the MFS and the MPS, and the latter is also called the hybrid Trefftz method (HTM) in Jirousek (1978, 1992, 1996) [1-3]. In Bogomolny (1985) [4] and Li (2009) [5] the error analysis of the MFS is given for Laplace's equation, and in Li (2012) [6] the error bounds of both MPS and HTM using particular solutions (PS) are provided for linear Elastostatics. In this paper, our efforts are devoted to explore the error analysis of the MFS and the HTM using fundamental solutions (FS). The key analysis is to derive the errors between FS and PS of the linear Elastostatics, where the expansions of the FS in Li et al. (2011) [7] are a basic tool in analysis. Then the optimal convergence rates can be achieved for the MFS and the HTM using FS. Recently, the MFS has been developed with numerous reports in computation; the analysis is behind. The analysis of the MFS for linear Elastostatics in this paper may narrow the existing gap between computation and theory of the MFS.
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New series expansions for fundamental solutions of linear Elastostatics in 2D
Computing, 2011Co-Authors: Ming-gong Lee, Jeng-tzong ChenAbstract:Series expansions of fundamental solutions are essential to algorithms and analysis of the null field method (NFM) and to analysis of the method of fundamental solutions (MFS). For linear Elastostatics, new Fourier series expansions of FS are derived, directly from integration. The new expansions of the FS are simpler than those in Chen et al. (J Mech 26(3):393–401, 2010 ), thus facile to application in NFM and MFS. The new series expansions of FS in this paper are important to both theory and computation of linear Elastostatics. Some computation of the MFS for linear Elastostatics is provided, where the expansions of fundamental solutions are a basis tool in analysis. Numerical results of a simple example are reported, accompanied with error analysis.
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Mixed types of boundary conditions at corners of linear Elastostatics and their numerical solutions
Engineering Analysis with Boundary Elements, 2011Co-Authors: Ming-gong Lee, Lih-jier Young, Po-chun ChuAbstract:Abstract The singular solutions at corners and the fundamental solution are essential in both theory and computation. Our recent efforts are made to seek the particular solutions of corner and crack singularity of linear Elastostatics, to design new models of corner singularity, and to find their numerical solutions. In [1] , [2] , a systematic analysis for singularity properties and particular solutions of linear Elastostatics is explored, and the singular solutions for corners with the displacement or the free traction boundary conditions have been found. This paper is a continued study of [1] , [2] , to explore new particular solutions for mixed types of boundary conditions at corners, which mean that the displacement and the free traction boundary conditions are subjected to the same corner edge in this paper. Explicit particular solutions have been found for any angle Θ ∈ ( 0 , 2 π ] ; this is distinct from [1] , [2] where the explicit solutions only with Θ = π and Θ = 2 π can be obtained. In this paper new singularity models with L-shaped domain and other non-rectangular domains are designed, and the highly accurate solutions are computed. Moreover, the singularity solutions as O ( r 1 / 4 ) and even O ( r 1 / 7 ) are found (Refs. [1] , [2] , [3] ). To our best knowledge, this is the first time to provide the particular solutions with different boundary conditions on the same corner edge in linear Elastostatics. The new particular solutions, new singularity, analysis, and computation in this paper are important for both theory and computation of linear Elastostatics.
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Combined Trefftz methods of particular and fundamental solutions for corner and crack singularity of linear Elastostatics
Engineering Analysis with Boundary Elements, 2010Co-Authors: Ming-gong Lee, Lih-jier Young, Po-chun ChuAbstract:Abstract The singular solutions at corners and the fundamental solutions are essential in both theory and computation. Our recent efforts are made to seek new models of corner and crack singularity of linear Elastostatics and their numerical solutions. In Li et al. (2009) [43] , a systematic analysis for singularity properties and particular solutions of linear Elastostatics is explored. This paper is a continued study of Li et al. (2009) [43] , general singular solutions for corners with free traction boundary conditions are derived. Both particular solutions and fundamental solutions are explored for plane strain and plane stress problems, and the singular solutions are derived directly from linear Elastostatics. Two new models (symmetric and anti-symmetric) of interior crack singularities are proposed, and their highly accurate solutions can be found by the collocation Trefftz method. Moreover, for the corner and crack singularity problems, the combined methods by using many fundamental solutions, but by adding a few singular solutions are proposed. Such a kind of combined methods is significant for linear Elastostatics with corners (i.e., the L-shaped domain), because the singular solutions can be obtained only by seeking the power ν k of r ν k numerically (as shown in Li et al., 2009 [43] ). Hence, only a few singular solutions used may greatly simplify the numerical algorithms, thus to enrich the numerical solutions of linear Elastostatics with corners, and to extend the method of fundamental solutions (MFS) for singularity problems.
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Models of corner and crack singularity of linear Elastostatics and their numerical solutions
Engineering Analysis with Boundary Elements, 2010Co-Authors: Po-chun Chu, Lih-jier Young, Ming-gong LeeAbstract:The singular solutions for linear Elastostatics at corners are essential in both theory and computation. In this paper we seek the singular solutions for corners with the clamped and the free stress boundary conditions, and explore corner singularity in detail. In this paper the singular solutions of linear Elastostatics are derived, and two new models of interior crack singularity are proposed. The collocation Trefftz methods are used to obtain highly accurate solutions, where the leading coefficient has 14 (or 12) significant digits by the computation with double precision. Such solutions are useful to examine other numerical methods for singularity problems in linear Elastostatics. Also the explicit singular solutions can be adapted to design and develop efficient numerical methods for singularity problems, such as the combined method (Li, 1998, 2008 [19,20]) and the Trefftz methods which include the boundary approximation method (Li, 1990, Li et al., 1987 [18,26]), the collocation Trefftz method (Li et al., 2008 [24]), the hybrid Trefftz method (Qin, 2000 [36]), the boundary collocation techniques (Kolodziej and Zielinski, 2009 [16]), etc. This paper also explores a systematic analysis for singularity properties and explicit singular solutions for corners of linear Elastostatics.
Po-chun Chu - One of the best experts on this subject based on the ideXlab platform.
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Mixed types of boundary conditions at corners of linear Elastostatics and their numerical solutions
Engineering Analysis with Boundary Elements, 2011Co-Authors: Ming-gong Lee, Lih-jier Young, Po-chun ChuAbstract:Abstract The singular solutions at corners and the fundamental solution are essential in both theory and computation. Our recent efforts are made to seek the particular solutions of corner and crack singularity of linear Elastostatics, to design new models of corner singularity, and to find their numerical solutions. In [1] , [2] , a systematic analysis for singularity properties and particular solutions of linear Elastostatics is explored, and the singular solutions for corners with the displacement or the free traction boundary conditions have been found. This paper is a continued study of [1] , [2] , to explore new particular solutions for mixed types of boundary conditions at corners, which mean that the displacement and the free traction boundary conditions are subjected to the same corner edge in this paper. Explicit particular solutions have been found for any angle Θ ∈ ( 0 , 2 π ] ; this is distinct from [1] , [2] where the explicit solutions only with Θ = π and Θ = 2 π can be obtained. In this paper new singularity models with L-shaped domain and other non-rectangular domains are designed, and the highly accurate solutions are computed. Moreover, the singularity solutions as O ( r 1 / 4 ) and even O ( r 1 / 7 ) are found (Refs. [1] , [2] , [3] ). To our best knowledge, this is the first time to provide the particular solutions with different boundary conditions on the same corner edge in linear Elastostatics. The new particular solutions, new singularity, analysis, and computation in this paper are important for both theory and computation of linear Elastostatics.
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Combined Trefftz methods of particular and fundamental solutions for corner and crack singularity of linear Elastostatics
Engineering Analysis with Boundary Elements, 2010Co-Authors: Ming-gong Lee, Lih-jier Young, Po-chun ChuAbstract:Abstract The singular solutions at corners and the fundamental solutions are essential in both theory and computation. Our recent efforts are made to seek new models of corner and crack singularity of linear Elastostatics and their numerical solutions. In Li et al. (2009) [43] , a systematic analysis for singularity properties and particular solutions of linear Elastostatics is explored. This paper is a continued study of Li et al. (2009) [43] , general singular solutions for corners with free traction boundary conditions are derived. Both particular solutions and fundamental solutions are explored for plane strain and plane stress problems, and the singular solutions are derived directly from linear Elastostatics. Two new models (symmetric and anti-symmetric) of interior crack singularities are proposed, and their highly accurate solutions can be found by the collocation Trefftz method. Moreover, for the corner and crack singularity problems, the combined methods by using many fundamental solutions, but by adding a few singular solutions are proposed. Such a kind of combined methods is significant for linear Elastostatics with corners (i.e., the L-shaped domain), because the singular solutions can be obtained only by seeking the power ν k of r ν k numerically (as shown in Li et al., 2009 [43] ). Hence, only a few singular solutions used may greatly simplify the numerical algorithms, thus to enrich the numerical solutions of linear Elastostatics with corners, and to extend the method of fundamental solutions (MFS) for singularity problems.
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Models of corner and crack singularity of linear Elastostatics and their numerical solutions
Engineering Analysis with Boundary Elements, 2010Co-Authors: Po-chun Chu, Lih-jier Young, Ming-gong LeeAbstract:The singular solutions for linear Elastostatics at corners are essential in both theory and computation. In this paper we seek the singular solutions for corners with the clamped and the free stress boundary conditions, and explore corner singularity in detail. In this paper the singular solutions of linear Elastostatics are derived, and two new models of interior crack singularity are proposed. The collocation Trefftz methods are used to obtain highly accurate solutions, where the leading coefficient has 14 (or 12) significant digits by the computation with double precision. Such solutions are useful to examine other numerical methods for singularity problems in linear Elastostatics. Also the explicit singular solutions can be adapted to design and develop efficient numerical methods for singularity problems, such as the combined method (Li, 1998, 2008 [19,20]) and the Trefftz methods which include the boundary approximation method (Li, 1990, Li et al., 1987 [18,26]), the collocation Trefftz method (Li et al., 2008 [24]), the hybrid Trefftz method (Qin, 2000 [36]), the boundary collocation techniques (Kolodziej and Zielinski, 2009 [16]), etc. This paper also explores a systematic analysis for singularity properties and explicit singular solutions for corners of linear Elastostatics.
L J Gray - One of the best experts on this subject based on the ideXlab platform.
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transient analysis of the dynamic stress intensity factors using sgbem for frequency domain elastodynamics
Computer Methods in Applied Mechanics and Engineering, 2010Co-Authors: A V Phan, L J Gray, Alberto SalvadoriAbstract:In this paper, a two-dimensional symmetric-Galerkin boundary integral formulation for elastodynamic fracture analysis in the frequency domain is described. The numerical implementation is carried out with quadratic elements, allowing the use of an improved quarter-point element for accurately determining frequency responses of the dynamic stress intensity factors (DSIFs). To deal with singular and hypersingular integrals, the formulation is decomposed into two parts: the first part is identical to that for Elastostatics while the second part contains at most logarithmic singularities. The treatment of the elastostatic singular and hypersingular singular integrals employs an exterior limit to the boundary, while the weakly singular integrals in the second part are handled by Gauss quadrature. Time histories (transient responses) of the DSIFs can be obtained in a post-processing step by applying the standard fast Fourier transform (FFT) and algorithm to the frequency responses of these DSIFs. Several test examples are presented for the calculation of the DSIFs due to two types of impact loading: Heaviside step loading and blast loading. The results suggest that the combination of the symmetric-Galerkin boundary element method and standard FFT algorithms in determining transient responses of the DSIFs is a robust and effective technique.
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symmetric galerkin boundary element analysis of the dynamic stress intensity factors in the frequency domain
Mechanics Research Communications, 2010Co-Authors: A V Phan, L J Gray, Alberto SalvadoriAbstract:A two-dimensional symmetric-Galerkin boundary integral formulation for the analysis of the dynamic stress intensity factors (DSIFs) in the frequency domain is described. A quadratic element is employed, allowing the use of the modified quarter-point element at the crack tip. For singular and hypersingular integrals, this formulation is decomposed into two parts: the first part is identical to those for Elastostatics while the second part, at most, contains only logarithmic singularities. The treatment of the elastostatic singular and hypersingular integrals is carried out by means of an exterior limit to the boundary, while the weakly singular integrals in the second part are handled by Gauss quadrature. Test examples are presented for the calculation of the DSIFs due to harmonic loading as well as wave scattering from a crack.
-
Symmetric-Galerkin Boundary Element Transient Analysis of the DSIFs for the Interaction of a Crack with a Circular Inclusion
Key Engineering Materials, 2010Co-Authors: A V Phan, L J Gray, Alberto SalvadoriAbstract:A dynamic analysis of crack-inclusion interaction is described in this paper. The analysis employs a two-dimensional symmetric-Galerkin boundary integral formulation for multi-domain elastodynamic fracture analysis in the frequency domain. The multi-domain technique is based on the assumption of perfectly bonded inclusions. The numerical implementation of this boundary integral formulation is carried out with standard quadratic elements, allowing the use of an improved quarter-point element for accurately determining frequency responses of the dynamic stress intensity factors (DSIFs). To deal with singular and hypersingular integrals, the formulation is decomposed into two parts: the rst part is identical to that for Elastostatics while the second part contains at most logarithmic singularities. The treatment of the elastostatic singular and hypersingular singular integrals employs an exterior limit to the boundary, while the weakly singular integrals in the second part are handled by Gauss quadrature. Time histories (transient responses) of the DSIFs are obtained in a post-processing step by applying the fast Fourier transform (FFT) and inverse FFT to the frequency responses of these DSIFs. Two numerical examples are presented for the computation of the DSIFs due to crack-inclusion interaction under two types of impact loading: Heaviside step loading and blast loading. The numerical results are consistent and con rm the well known crack tip shielding mechanism observed during the interaction between a crack and a much sti er inclusion.