Boundary Element Analysis of Two-Dimensional Thin Anisotropic Composites with Thermal Effects

Abstract

The main study of the thesis is for applying the boundary element method (BEM) to study the two-dimensional anisotropic thermoelasticity of composites when layers of the structures are very thin Under the circumference when the source point on one surface is very close to integration elements on the opposite surface of thin layers the well known issue of “nearly singular integration” in the BEM will arise causing instability in numerical integrations As a result the BEM will fail to properly analyze the thermoelaticity of thin anisotropic composites For thermoelaticity the thermal effect will lead to a domain integral in the boundary integral equation For avoiding direct integration the domain integral has been analytically transformed to surface ones In the thesis the nearly singular integrals are regularized by the scheme of integration by parts Furthermore an additional numerical difficulty arises in numerically evaluating the transformed boundary integrals whose integrands are associated with trigonometric functions Under the condition of nearly singular integration the integrands shall fluctuate drastically near the projection point of the source posing difficulty in numerical evaluation This problem is overcome by the approach of domain sub-division near the projection point and moreover increased numbers of Gauss points are required A few benchmark examples are investigated by the implemented BEM code All BEM results turn out to agree with those obtained by ANSYS based on the finite element method

Date of Award	2019
Original language	English
Supervisor	Yui-Chuin Shiah (Supervisor)