Application of Linear Constraint Approximations to Frame Structures,
GENERAL MOTORS RESEARCH LABS WARREN MICH
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The use of structural approximation techniques coupled with mathematical programming methods has proved to be an efficient way to handle structural optimization problems. Approximating the constraints with first order Taylor series implies that the effectiveness of the approximation is dependent on the linearity of the active constraint over some segment of the design space. This is accomplished by choosing either a simple element, such as a truss or shear panel, or by using an intermediate design variable chosen for the particular application. This approach has been applied to frame models of the automotive skeleton. The beams were thin-walled box and channel sections in which thickness, widths, and heights were used as design variables. It was found that approximately 20-25 finite element solutions were required to find minimum mass solutions for reasonably complex structures with approximately 500 degrees of freedom and 100 design variables with both stress and stiffness constraints. Since the majority of the analyses are required in the convergence portion of the problem, the effect of changing the move limits was minimal. However, if the move limits were too large, the process did not converge.