Fuzzy Boundary Element Method with Uncertain Shear Modulus in Linear Plane Strain Elasticity

Engineering systems are often too complex and their behavior cannot be determined using closed form or exact methods. To circumvent this problem, numerical methods, such as boundary element method, have been formulated to obtain approximate solutions to partial differential equations, which describe the behavior of the physical engineering systems. However, the inherent uncertainty in constitutive formulation causes uncertainties in the solutions obtained by numerical methods and undermines their validity. Conventional analysis does not account for material uncertainty, which is, however, accounted for in the design phase. This paper addresses the impact of uncertain shear modulus for plane strain linear elasticity problems on the numerical solutions obtained using boundary element method. The uncertainty is modeled using fuzzy approach. Matrix parameterization is developed to obtain exact worst case bounds on the solutions assuming that a correct partial membership function is given. Numerical examples are presented to illustrate the behavior of the method.