A new boundary element technique without domain integrals for elastoplastic solids (original) (raw)
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This paper presents an assessment and comparison of boundary element method (BEM) formulations for elastoplasticity using both the consistent tangent operator (CTO) and the continuum tangent operator (CON). These operators are integrated into a single computational implementation using linear or quadratic elements for both boundary and domain discretizations. This computational setting is also used in the development of a method for calculating the J integral, which is an important parameter in (nonlinear) fracture mechanics. Various two-dimensional examples are given and relevant response parameters such as the residual norm, computational processing time, and results obtained at various load and iteration steps, are provided. The examples include fracture problems and J integral evaluation. Finally, conclusions are inferred and extensions of this work are discussed. Ó
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International Journal of Mechanical Engineering and Technology (IJMET), 2018
This work is the development of boundary element method for elastoplastic plate analysis to include elastic-linear hardening material. The plate is subjected to bending, in-plane and combined bending and in-plane. The plastic zone is evaluated by using von Mises criterion. The cell discretization is implemented to solve numerically the domain integral caused by plasticity. To evaluate the nonlinear term in the formulation of the boundary element, a total incremental technique is implemented. The capability of the development in this work will be presented by having numerical examples.
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Boundary and finite element methodologies for the determination of the response of inelastic plates are compared and critically discussed. Flexural dynamic plate bending problems are considered and a hardening elastoplastic constitutive model is used to describe material behaviour. The domain/boundary element methodology using linear boundary and quadratic interior elements and the finite element method with quadratic Mindlin plate elements are used in this work. The discretized equations of motion in both methodologies are solved by an efficient step-by-step time integration algorithm. Numerical results obtained are presented and compared in order to access the accuracy and computational efficiency of the two methods. In order to make the comparison as meaningful as possible, boundary and finite element computer codes developed by the author are used in this paper. In general, boundary elements appear to be a better choice than finite elements with respect to computational efficiency for the same level of accuracy.
Boundary elements: new developments in elastoplastic analysis
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This paper presents the complete implementation of the half-plane fundamental solution for elastoplastic problems. This original formulation has proved to be very efficient for problems concerning the semi-plane and is applicable to a wide range of engineering problems such as soil-structure interaction, tunnels, trenches, etc., where, due to its very nature, the satisfaction of the traction-free condition is automatically accomplished without the need for boundary elements over the surface of the half-plane. In addition, a comparison between approximate procedures and the proper integral equation for computing stresses at internal points is discussed in the light of computer efficiency. The latter is found to be preferable not only because it requires fewer operations per iteration cycle, but also for producing more accurate results. Finally examples are presented to illustrate the theory described in the text.
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The main objective of this paper is to present a general three-dimensional boundary element methodology for solving transient dynamic elastoplastic problems. The elastostatic fundamental solution is used in writing the integral representation and this creates in addition to the surface integrals, volume integrals due to inertia and inelasticity. Thus, an interior discretization in addition to the usual surface discretization is necessary. Isoparametric linear quadrilateral elements are used for the surface discretization and isoparametric linear hexahedra for the interior discretization. Advanced numerical integration techniques for singular and nearly singular integrals are employed. Houbolt's step-bystep numerical time integration algorithm is used to provide the dynamic response. Numerical examples are presented to illustrate the method and demonstrate its accuracy. Ó
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International Journal for Numerical Methods in Engineering, 1986
An advanced formulation of the boundary element method has been developed for inelastic analysis based on an initial stress approach. The iterative solution algorithm makes use of an accelerated initial stress approach in which the past history of initial stresses are used to obtain an initial estimate for the current increment. In the present analysis the geometry and functions are represented by higher order (quadratic) shape functions to model complex geometries and rapid functional variations accurately. The methods of numerical integration of the kernels, particularly the singular type, are substantially improved by devising suitable automatic sub-segmentation routines that incorporate the recent developments in mapping procedures. The formulations have been implemented for two-dimensional plane stress, plane strain and three-dimensional elasto-plasticity problems.
Boundary element formulation in finite deformation plasticity using implicit integration
Computers & Structures, 1989
A Boundary Element Method is developed for the solution of large strain problems. Betti's reciprocal theorem relevant to an Updated Lagrangian formulation is established as the basis for the boundary element formulation. Fully implicit integration of the constitutive relations leads to a nonlinear virtual work equation in each increment, which is solved by iteration. In each such equilibrium equation the elastic operator is isolated, and so the Boundary Element Method can be conveniently used. A system of equations is solved with all nonlinear terms assembled on the right hand side. A numerical example shows application to the stretching of a metal sheet. Elastic and plastic cross-anisotropy (the stressed plane is isotropic) and complete incompressibility are assumed. Hill's yield criterion is adopted together with isotropic hardening.