Complex engineering problems need appropriate constitutive laws such as Disturbed State Concept (DSC), as well as robust accurate computational analysis methods such as adaptive and stochastic finite element methods (FEM). DSC provides a unified basis for constitutive modeling including elastic, plastic and creep deformations, microcracking, damage and softening, stiffening, and cyclic fatigue under thermomechanical loading. It includes intrinsical regularization, localization, characteristic dimension and avoidance of spurious mesh dependence. It also leads to new procedures for adaptive FEM and stochastic FEM. Adaptive FEM is a method to adapt or guide itself to better subsequent computation by use of previous computational information so as to achieve prescribed accuracy. It's a powerful procedure for analyzing deformation of special problems such as interfaces and joints and shear bands, and complex materials with both hardening and softening. An adaptive finite element procedure with combined Disturbance-Hybrid stress error estimator/remeshing indicator is proposed and tested by comparing with some published results, and the corresponding user-interactive unified DSC finite element program with more than 10 options is developed and applied to thermal analysis of electronic packaging problems. Unlike deterministic analysis methods, stochastic FEM approach further considers the random variations of involved parameters to further make the deterministic constitutive and numerical modeling more realistic in a statistical manner. Traditional stochastic FEM is reviewed and a new efficient DSC stochastic FEM is formulated for reliability analysis of electronic packaging problems. The computer visualization and animation are applied to display the computed results for the purpose of easier use and interpretation of the results, which will be one of major trends for engineering application of computational methods. In this dissertation, combined study is carried out from a comprehensive (computational and constitutive) viewpoint, and the practical and academic values of the adaptive and stochastic DSC finite element procedures for electronic packaging problems will be demonstrated.
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