Topology Optimization (TO) of static structures with fixed loading is a very interesting topic in structural mechanics that has found many applications in industrial design tasks. The extension of the theory to dynamic loading for designing a Multibody System (MBS) with bodies which are lighter and stronger can be of high interest. The objective of this thesis work is to investigate one of the possible ways of extending the theory of the static structural Topology Optimization to Topology Optimization of dynamical bodies embedded in a Multibody System (TOMBS) with large rotational and transitional motion. The TOMBS is performed for all flexible bodies simultaneously based on the overall system dynamical response. Simulation of the MBS behavior is done using the finite element formalism and modal reduction. A modified formulation of Solid Isometric Material with Penalization (SIMP) method is suggested to avoid numerical instabilities and non-convergence of the optimization algorithm implemented for TOMBS. The nonlinear differential algebraic equation of motion is solved numerically using Backward Differential Formula (BDF) with variable step size in SundialsTB and Assimulo integrators implemented in Matlab and Python. The approach can find many applications in designing vehicle systems, high speed robotic manipulators, airplanes and space structures. Also, to show the current capability of the tools in the industry to design a body under dynamic loading using the multiple static load cases, the lower A-arm of double wishbone suspension system is designed in Abaqus/TOSCA, where, the loads are collected from rigid multibody simulation in Dymola.In everyday life, people deal with different kinds of mechanical machines and mechanisms. These mechanisms are a set of mechanical and electrical parts designed to perform a specific task. Among the others, the task of a mechanical part is to carry a load or transfer it. The key question a designer should ask is how to design the part in terms of the shape, material, weight, etc. in order for the part to be optimal. This is a question that can be answered using structural optimization. Particularly in this thesis work it is tried to suggest an algorithm for optimizing the shape or material distribution of the parts within a multibody system. The method is called topology optimization of multibody system. The behavior of the system as a whole is considered to design each individual mechanical part
