Meshless thermo‐elastoplastic analysis by triple‐reciprocity boundary element method

Abstract

SUMMARYIn general, internal cells are required to solve thermo-elastoplasticity problems by a conventional boundary element method (BEM). However, in this case, the merit of BEM, which is the easy preparation of data, is lost. A conventional multiple-reciprocity boundary element method (MRBEM) cannot be used to solve elastoplasticity problems, because the distribution of initial strain or stress cannot be determined analytically. In this study, it is shown that without the use of internal cells, two-dimensional thermoelastoplasticity problems can be solved by a triple-reciprocity BEM using a thin plate spline. Initial strain and stress formulations are adopted and the initial strain or stress distribution is interpolated using boundary integral equations. A new computer program was developed and applied to solve several problems.

A Fast Reduced-Order Model for Radial Integration Boundary Element Method Based on Proper Orthogonal Decomposition in the Non-Uniform Coupled Thermoelastic Problems

“…While DRM is extensively used, it can be challenging to implement if the kernel functions of certain domain integrals in the integral equations do not match the fundamental solution of the problem. This is indeed the primary reason why DRM is not easily applicable to solving elastoplastic problems [43]. Therefore, we adopt the radial integral method (RIM), which transforms the domain integrals containing the unknown functions into equivalent boundary integrals, forming a pure boundary element algorithm.…”

Three-Dimensional Boundary Element Strategy for Stress Sensitivity of Fractional-Order Thermo-Elastoplastic Ultrasonic Wave Propagation Problems of Anisotropic Fiber-Reinforced Polymer Composite Material

“…) is interpolated. Using the Green's second identity and Equation (37), the following result is obtained [8,9]:…”

“…This method allows for a very accurate solution to be produced using only fundamental low-order solutions and reduces the requirements for data preparation. Ochiai [ 9 ] applied the triple-reciprocity BEM to solve 2D thermo-elastoplastic problems with an arbitrary distributed heat source [ 10 ] and three-dimensional elastoplastic problems with initial strain formulas [ 10 ]. Recently, Fahmy et al [ 11 , 12 , 13 , 14 ] developed fractional BEM schemes to solve certain thermoelastic problems.…”

Three-dimensional thermo-elastoplastic analysis by triple-reciprocity boundary element method

“…Although the fundamental solutions for the initial stress formulation are simpler than those for the initial strain formulation, the CPU time is almost the same. The CPU time is 131 s using the computer program code for two-dimensional case [10]. The tree-dimensional computer program code, which is developed to clearly demonstrate the theory, must be improved for practical use.…”

“…Ochiai and Kobayashi [9] applied the triple-reciprocity BEM without using internal cells to two-dimensional elastoplastic problems using initial strain formulations. Ochiai applied the triple-reciprocity BEM to two-dimensional thermoelastoplastic problems with arbitrary heat generation [10] and three-dimensional elastoplastic problems using initial strain formulations [11]. Only the triple-reciprocity BEM and the local boundary element method have been applied to elastoplastic problems without internal cells.…”