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analysis asymptotic BIE and BIDE BIE given body force boundary conditions boundary element method boundary integral equations boundary integral formulation Cauchy principal value coefficients components computed considered constants coordinate system crack problems crack tip defined deflection denotes derived differential equations dimensionless discretized BIE displacement discontinuities displacements and tractions divergence theorem elastic elastodynamics elastostatics finite fracture mechanics functions fundamental solutions Gaussian quadrature Gaussian quadrature rule given by equations Hence infinite integral kernels internal boundary-value problem internal points intrinsic coordinate inversion Laplace transform Laplace transform domain linear load micropolar thermoelasticity nodal points nodes notations obtain plane plate polynomials principal value integrals principal value sense quadratic quadrature rule regular Gaussian quadrature regularized integral representation shown in Fig singular element Sladek solved strain strain tensor stress tensor stress-intensity factor symmetry theory three dimensions three-dimensional problems time-dependent tion two-dimensional problems unknowns viscoelastic write