Study On Topology Optimization Of Complex Mechanics Structure

Growing global competition in advanced manufacture demands continuous innovations in the design of engineering components. Continuum structural topology optimization is an increasingly powerful method which can be used to optimize the material arrangements in design domain to achieve a wide variety of performance objectives. Presently, topology optimization techniques for continuum structures are mainly concentrating on single objective optimization problems and regular design domain. However, in practical engineering fields, there exist lots of topology optimization problems with complicate objective, irregular design domain and other restriction conditions. Therefore, it is important to study topology optimization of structure satisfying the assembly requirements and stability requirements, etc.In this work, research in structural topology optimization with a foundation on 3D geometric modeling with NURBS method, continuum mechanics, the finite element analysis, solid isotropic material with penalization method and optimization methods, is presented to satisfy the demand along with the advancements in manufacture technology. An efficient geometrical boundary description methodology has been developed for structural topology optimization under assembly constraints in engineering. A stress criterion for the SIMP model is introduced as stability constraints of structure, which is expressed as a constraint of the von Mises equivalent stress. Using the described algorithm, the initial structural topology parametric figure is derived for putting the topology optimization structure into reality by present manufacture technology. Base on SIMP method and the governing differential equations of structure in continuum mechanics, the mathematical formulation of topology optimization problems is presented, which has static or dynamic objective and is under geometric or stress constraints. Optimality criteria and sequential quadratic programming method are applied to solve these topology optimization problems with different objective and constraints. A number of implementation aspects and ways to solve the optimization problem generated in optimization process, such as checkboard patterns and mesh-dependency, are discussed in more detail. Application of the proposed methodology has been investigated for the topology optimization of three dimension structure with objectives in respect of minimal compliance, fundemantal frequency and compliant mechanism, respectively. By extending these above methodology to particular application, they have been demonstrated to be worth. The main contents of this dissertation are organized as follows: In order to satisfy the assembly requirement of engineering components, a geometrical boundary definition of the design domain for the topology optimization structure is derived by the use of a set of partial differential equations and cost function. A stress criterion for the SIMP model expressed as a constraint of the von Mises equivalent stress is introduced to be stability constraints of structure. Local stress constraints with relaxation and global stress constaints for topology optimization problem are studied, respectively. A smooth model of topology optimization for three dimenstion structure, which has compliance minimization objective considering stress, volumetric and geometric constraints simultaneously, is proposed. Optimality criteria method is applied to solve the proposed topology optimization problem. The singularity aspects generated in topology optimization process, such as checkboard patterns and mesh-dependency, are resolved by filtering the objective sensitivity. This above method for topology optimization of three dimension structure is demonstrated by the design of wheel under load and boundary constraints.One of the important applications of topology optimization method is in eigenvalue optimization for vibration. Based on dynamic mechanics theory and the finite element method, the governing differential equations for structure subjected to dynamic loads, and the fundamental eigenvalue as the objective of structure are presented. A mathematical model of topology optimization for three dimenstion dynamically loaded structure, which has the fundamental eigenvalue equal to the specified value, is proposed. Sequential quadratic programming method is applied to solve this topology optimization problem with sensitivity analysis of objective to design variables. The aerodynamics of wing is obtained by study on three-dimension Navier-Stokes numerical simulation. The topology optimization of wing faced to experimental demand is investigated by the proposed method optimization of dynamically loaded structure.Compliant mechanism is another dominant application of topology optimization of structure, and it has been developed for important micro manipulator in electronics, information technology and bioengineering. By specifying the initial structural topology parametric figure, the final topology optimization of structure is governed by the designer so that three- dimension structure is interpretable and manufacturable. The formulation of output displacements of optimization structure is achieved by adjoint approach in the finite element method. The mathematical model of topology optimization for compliant mechanisms is established on the base of the principle of mutual energy, which has geometric advantage as the objective. The analytical expression of objective sensitivity to design variables is deduced. This above method for topology optimization of compliant mechanism is demonstrated by the design of three dimension microgripper.