Keywords: topology optimization, modal strain energy, CATO algorithm, shell structure, artificial material model, solid finite element.

A three-dimensional topology optimization technique is proposed to consider both static and dynamic characteristics of the structure in a design optimization process. The solid finite element technologies are consistently used to calculate the physical response of structures such as stresses and natural frequencies. In particular, the enhanced assumed strain lower order solid finite element is adopted to produce accurate numerical analysis results and to have high computational efficiency. In this study, both the elastic strain energy and the modal strain energy terms are employed as the objective function to deal with the static characteristic of structures as well as its dynamic characteristics. Therefore, the strain energy based resizing algorithm is successfully used for both the static and dynamic problems. The initial volume of structures is introduced as the constraint function. The adopted updating scheme is based on the CATO algorithm so that the proposed technique can deal with many design variables without particular difficulties. On the other hand, the artificial material model is adopted to produce clearer and more distinct structural topologies. The material is characterized by a density parameter that is defined in terms of the volume of the voided zone, which is assumed as the cube cell that is centrally placed in the solid finite element. In this study, multi-objective problems are tackled with the use of a weight function. Therefore, some meaningful observation in the material redistribution of the structure against external loads and self-vibrations has been provided. The capability of the proposed technique is thoroughly tested with several topology optimization problems for plate and shell structures. From the numerical results, it is found to be that the proposed techniques are extremely useful and the final optimum topologies have been greatly affected by the consideration of the dynamic characteristics of the structures. Finally, we found that the present technique is highly applicable to design optimization problems, in which both the static and the dynamic characteristics of various types of structures is simultaneously controlled and improved.

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