Search

This paper presents a concurrent topology optimization approach for simultaneous design of composite structures and their periodic material microstructures with three or more phases. The effective properties of multi-phase materials are obtained via homogenization technique which serves as a bridge of the finite element models of the macrostructure and the material microstructure. The base materials of periodic microstructures used in each phase of the macrostructure are divided into several groups and sensitivity analysis are carried out on them one by one. Meanwhile, the sensitivity number at the macrostructure is derived which is coupled with the designed material properties. Then, the composite configurations of material microstructures and macrostructures are inversely optimized concurrently based on the bi-directional evolutionary structural optimization (BESO) algorithm. Several 2D and 3D numerical examples are presented to demonstrate the effectiveness of proposed design approach.

Presenting a stabilized nodal integration method for analysis of Reissner-Mindlin plate.Squared-residual of equilibrium equations are considered in the potential energy functional.Giving an empirical value range of stabilization parameter through numerical tests.Numerical examples shown efficiency of the new method to improve calculation accuracy.The proposed scheme can eliminates the temporal instability successfully. In this paper, a temporal stabilized nodal integration method (sNIM) using 3-node triangular elements is formulated for elastic-static, free vibration and buckling analyses of Reissner-Mindlin plates. Two stabilization terms are added into the smoothed potential energy functional of the original nodal integration, consisting of squared-residual of equilibrium equations. A gradient smoothing technique (GST) is used to relax the continuity requirement of shape function. The smoothed Galerkin weak form is employed to create discretized system equations, and the node-based smoothing domains are formed to perform the smoothing operation and the numerical integration. A stabilization parameter is finally introduced to the modified system for the sake of curing temporal instability. Numerical tests provide an empirical value range of stabilization parameter, within which very accurate and stable results can be obtained for both static and eigenvalue problems.

The free vibration problem of unsymmetrical sandwich plates with laminated composite faces and orthotropic core is analysed in the consideration of the effects of bending, transverse shear, plane inertia, rotatory inertia, and coupling inertia. The spline finite point method (SFPM) is selected to solve the present problem and to establish the basic formulae for a computer programme that can be run on microcomputer. A lot of numerical examples of the cross-ply face sandwich plates, with various boundary conditions, are obtained by the present method to make clear for coupling effects of composite material plates and to seek the optimum ply design of engineering structures.