Probabilistic BEM for elastodynamic problems

Solution of elastodynamic problems involving elastic materials with random material properties are addressed in this paper. Boundary integral equation formulations using particular integrals are presented for the solution of both free vibration problems and transient elastodynamic problems. In both the cases, the domain integral which appears due to the presence of the inertia term is converted to a surface integral by approximating the inertia term using certain known functions and a fictitious density function. A new probabilistic boundary element method is proposed to study the effects of randomness in material properties such as modulus of elasticity, mass density etc. which are treated as independent random variables. Perturbation technique is adopted to obtain the recursive equations needed for the probabilistic analyses. Numerical results are presented to demonstrate the variability of the response due to randomness in material properties.