TABLE OF CONTENTS Changes in the topology and the geometry of the structure are encountered particularly in layout optimization problems [e.g. [1]]. Layout optimization means the simultaneous selection of the optimal variables describing
the topology (i.e. spatial sequence of members and joints);
the geometry (i.e. the location of joints); and
the cross-sectional dimensions (sizing).
Layout optimization is perhaps the most challenging class of problems in structural optimization because there exists a large number of possible topologies and they are difficult to classify and quantify. Moreover, at each point of the available space, potential members may run in a large number of directions. At the same time, layout optimization is of considerable importance because it results in much greater material savings than pure cross-section optimization.
Layout optimization is usually based on a ground structure, which is the union of all potential members. During the optimization procedure, non-optimal members are eliminated and the optimal size of the remaining members is determined. From the viewpoint of the ground structure approach, layout optimization can also be defined as a special case of cross-section sizing optimization in which cross-sectional areas may take on a zero value. An alternative to this approach is an incremental synthesis approach in which, starting with a few members, new members and joints are progressively added.
Because of the complexity in simultaneous optimization of the geometry, the topology and the cross sections, two classes of problems are often considered in optimization of the structural layout:
Topological optimization, where members are usually...
