The novel boundary integral equation with adaptive orthogonal IMLS based line integration method for cracked domains under thermal stress

Abstract For finite cracked domain under unknown thermal field distribution, based on the direct boundary element method (BEM) and the displacement discontinuity method (DDM), a set of novel boundary integral equations (BIEs) are derived. The main BIE is derived based on the displacement BIE, followed by two supplementary equations for ensuring enough equations as the unknowns on crack are considered. Besides, the two supplementary BIEs are alternatively used depending on the type of known quantities, traction or displacement. The thermal field is simulated by heat conduction BIEs firstly, then thermal stress analysis for cracked domains is performed by the new derived thermo-elastic BIEs. To treat the domain integrals caused by considering the thermal field, the adaptive orthogonal interpolating moving least-square (IMLS) method based line integration method (AOIMLS-LIM) is proposed for domain integrals containing unknown functions. With AOIMLS-LIM, domain integrals are reduced into boundary integrals with line integrals dimensionally and calculated by adding the line integrals up next. All the necessary temperature values for the line integral points can be interpolated from discretize nodes. The AOIMLS method can avoid singular moment matrices while calculating its shape functions, besides, the shape functions own a vital property, i.e., the interpolating property.