Ernest Hinton

Homogenization Theory for Media with Periodic Structure

In this chapter an overview of the theory of homogenization for composites with regular structure is presented. Periodicity and asymptotic expansion are desned and an application of homogenization to the simple case of a one dimensional elasticity problem is given. Derivation of the basic formulas for the general case of a boundary value problem in strong form is discussed. Finally, the homogenization equations for the elasticity problems in weak form for perforated media are derived.

Experiences In Topology Optimization of Plane Stress Problems

The outcome of the topology optimization process is insuenced by several factors: different material models, resizing schemes, finite element discretizations and element types. The optimal layout may also be affected by the resizing parameters. This chapter is mainly devoted to the study of the insuence of the above parameters. To demonstrate the usefulness of the method, several examples of a more practical nature are provided.

Topological Layout and Reinforcement Optimization of Plate Structures

In this chapter the homogenization method for plane stress problems is extended to deal with the creation of optimal layout and reinforcement topologies of plate structures. In this formulation the problem is to determine the stiffest plate strueture with a volume constraint for the reinforcement material. Introducing plate microcell models, a formulation for homogenization of plates based on the first order thick plate theory is presented. To solve the optimization problem the optimality criteria method is used. Using different material models some examples are provided.

Integrated Structural Optimization

An overview of the concept and modules of a three phase integrated structural optimization system is the subject of this Chapter. The topology optimization module provides Information about the Optimum layout and topology. In the image processing module by employing Computer vision techniques a structural model with smooth boundaries is extracted. In the third phase, using the conventional size and shape optimization methods the final optimal design is obtained. By constructing integrated design and optimization systems considerable improvement may be achieved by cutting development time and design costs.

Alternative Approaches to Structural Topology Optimization

This chapter is devoted to intuitive methods which are simple to implement and may be used as an alternative to topology optimization by the homogenization method. A method for Simulation of functional adaptation of bone mineralization in vertebrates is introduced and an algorithm based on effective stresses is presented. The evolutionary fully stressed method is also briefly explained.

Structural Topology Optimization using Optimality Criteria Methods

In this chapter, the basic concepts related to the optimality criteria methods are introduced. Then the mathematical model for the structural topology optimization problem is constructed. The optimality conditions are explained and an optimization procedure based on optimality criteria methods is presented. Resizing schemes for updating design variables are explained. The issue of the optimal orientation for the homogenized orthotropic material is discussed. The algorithm of the Computer program PLATO is explained and a few illustrative examples are presented.

Solution of Homogenization Equations for Topology Optimization

In this chapter motives for using the homogenization theory for topological structural optimization are briesy explained. Different material models are descrihed and the analytical Solution of the homogenization equations, derived in the last section of Chapter 2, for the so called ‘rank laminate composites’ is presented. The snite element formulation is explained for the material model based on a microstruciure consisting of an isotropic material with rectangular voids. Using the periodicity assumption, the boundary conditions are derived and the homogenization equation is solved. The results to be used in topology optimization are presented.