This thesis aims to improve the performance and to extend the applications of the Finite Cell Method (FCM). Some new integration methods are introduced in the thesis, such as modified weights and integration points, low order equivalent function and an adaptive integration scheme. Investigating different integration schemes in problems of solid mechanics presented in this thesis indicates that the introduced adaptive integration scheme is relatively an economic approach to gain accurate results. The research continues by applying the FCM for the problems of elastoplasticity for the flow theory with nonlinear isotropic hardening. This approach can stimulate the research into the simulation of different materially nonlinear problems using a simple background mesh. Numerical examples in two and three dimensions demonstrate the efficiency of the FCM and the proposed integration scheme at solving materially nonlinear problems. In addition, the FCM is numerically compared with an h -version FEM for the Prandtl-Reuss flow theory of plasticity. The results demonstrate the efficiency of the FCM to solve materially nonlinear problems. Finally, to provide a commercial and easily accessible ground, the FCM is implemented into ABAQUS. Keywords: Finite Cell Method, Numerical integration, Elastoplasticity.
