In this paper, the elastic behavior of uniform and functionally graded porous lattice structures made by a double pyramid dodecahedron unit cell is investigated. Analytical solutions are derived in order to estimate the elastic moduli of the proposed structures in two directions. The analytical solution is validated by finite element simulations and experimental tests while the results show good agreement in general. The average difference between the numerical and analytical values of elastic modulus is under 14.44%, while the average error of experimental test and analytical solution is 15.69%. A comprehensive optimization is performed by considering elastic moduli in two different directions as objective functions. Various uniform lattice structures with different relative densities are optimized using NSGA-II algorithm as well as lattice structures with graded distribution of porosity. A variety of optimal designs are achieved by multiobjective optimization algorithm and the best point of the Pareto front is selected by the TOPSIS method. Furthermore, the functionally graded lattice structures are optimized by considering desirable relative densities in each layer and applying constructive constraints. Different distribution patterns of relative density are considered in layers in order to present the flexible design capability of the developed structure. The obtained results show that the elastic modulus is significantly dependent on the relative density of each layer as well as cell configuration. Also, different lattice structures could be achieved by applying desirable prescribed distribution of properties. A comparison between optimized and base model indicated that elastic moduli was considerably improved in optimized models. In optimization of uniform models, was increased by 115%, 89%, and 69% in optimized structures for relative densities of 10%, 30%, and 50%, respectively. Moreover, was improved in optimized models by 27%, 24%, and 18% for relative densities of 10%, 30%, and 50%, respectively.
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