Truss optimization considering homologous deformation under multiple loadings

The deformation of a structure shall be called homologous, if a given geometrical relation holds for a given number of structural points before, during, and after the deformation. Some researchers have utilized the idea of structural design with the finite element method. The approaches use the decomposition of the FEM equation or equality equations to obtain homologous deformation. However, weight reduction and response constraints such as stress, displacement or natural frequency cannot be considered by those theories. An optimization method solving the above problems is suggested for obtaining homologous deformation. Homology constraints can be considered under multiple loading conditions as well as a single loading condition. A homology index is defined for multiple loading conditions. Examples are solved to demonstrate the performance of the method.