Boundary Element Method's Treatment of Interfacial Thermal Stresses Between Dissimilar Anisotropic Materials

Abstract

One of the most crucial concerns in the use of bonded composites lies in the interfacial thermal stresses developed between dissimilar materials as a result of the mismatch of thermal expansion coefficients. Although the boundary element method (BEM) has been recognized as an efficient computational tool, especially for rapidly varying stresses near the free edge of bonded composites, the study of the interfacial thermal stresses between dissimilar anisotropic materials by BEM still remains unexplored. An intercoupled BEM approach is proposed to investigate the interfacial thermal stresses by transforming the volume integral caused by thermal loading into a series of boundaries ones. Three numerical examples are provided as illustrations of the veracity as well as the applicability of the proposed scheme. NomenclatureA i j = complex constants depending on material properties C i j = geometrical coefficients at the source point C 0 = heat-source term K i j = heat-conductivity coefficients of anisotropic materials n k = components of the unit outward normal vector along the boundary P = source point on the boundary Q = field point on the boundary Q * = fundamental solution of the normal temperature gradient q = field point in the domain r i j = complex constants depending on material properties S = boundary surface T i j = fundamental solution for the traction t i = nodal tractions U i j = fundamental solution for the displacement u i = nodal displacements x pi = coordinates of the source point β = inclined angle of the outward normal measured from the x 1 axis γ ik = constant coefficients related to thermal properties of the material ζ = local coordinates of the field point = temperature change at the field point * = the fundamental solution of the temperature field µ i = complex root of the characteristic equation for anisotropic materials = domain region

BEM Stress Analysis for Thin Multilayered Composites Subjected to Inertial Loads

“…However, there is one more issue to be addressed for the validity of the regularized BIE. As described in details by Shiah and Lin [8], the branch cut of the multiple-value function log(z) needs to be redefined to be oriented outwards at the source point. The purpose of such a process is to avoid the intersection of the negative -axis through the domain, which will invalidate the volume integral transformation for the integral of the body force.…”