Morphing Evolutionary Structural Optimization (MESO) is the soft-kill version of the Evolutionary Structural Optimization (ESO). A particular attention has been paid to the shape optimization using the ESO and MESO over two past decades. Up to now, no precise theoretical base or mathematical proof for the convergence of ESO-based methods to optimum solution has been presented. For some structures like Michell trusses, a qualitative validation of the ESO by showing the similarity of the ESO results with the optimum shapes has already reflected in the literature. Moreover, only few researchers have investigated the quantitative validation of the ESO-based methods. In addition, the ESO-based methods have not been applied to problems in which their objectives are the overall deflection of the structure. This paper deals with the optimization of some structural elements for minimizing their overall deflections. The benchmark problems discussed here are plates and beams. Cantilever beams with different rectangular cross sections and simply supported and clamped plates have been considered in this study. These structures are acted upon the distribute loads and using finite element method, they are divided into some elements. The optimization problem is defined as minimization of the integral of the deflection over all nodes of these structures. Introducing new sensitivity numbers, the MESO is successfully applied for these problems and the numerical results reveal that the MESO method converges to the optimum in these problems. Furthermore, in the beam cases where the analytical solutions are available, the maximum difference between the MESO and the analytical solutions is 3.11%. It is concluded that the ESO based methods are amongst the powerful, reliable and robust optimization methods which have a very simple logic and can be easily implemented.

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