Optimum design of structures with stress and displacement constraints using the force method. (English) Zbl 1061.74043

Summary: A new structural analysis and optimization algorithm are developed to determine the minimum weight of structures with truss and beam-type members under displacement and stress constraints. The algorithm combines the mathematical programming based on sequential quadratic programming technique, and the finite element technique based on integrated force method. The equilibrium matrix is generated automatically through the finite element analysis while the compatibility matrix is obtained directly using the displacement-deformation relations and the single-valued decomposition technique. By combining equilibrium and compatibility matrices with force-displacement relations, the equations of equilibrium are obtained with element forces as variables. The proposed method is extremely efficient to optimize truss and beam structures under stress and displacement constraints. The computational effort required by the force method is found to be significantly lower than that of the displacement method. The effect of geometric nonlinearity in the structural optimization problems under stress and displacement constraints is also investigated, and it is illustrated that the geometric nonlinearity is not an important issue in these problems, and hence it does not affect the final optimum solution significantly. Four examples illustrate the procedure and allow to compare the results with those reported in the literature.


74P05 Compliance or weight optimization in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74S05 Finite element methods applied to problems in solid mechanics


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