Topology Optimization of Truss-Like Structure with Stress Constraints Under Multiple-Load Cases

A new method for topology optimization of truss-like structures with stress constraints under multiple-load cases(MLCs)is presented.A spatial truss-like material model with three families of orthotropic members is adopted,in which the three families of members along three orthotropic directions are embedded continuously in a weak matrix.The densities and directions of the three families of members at the nodes are taken as the design variables.An optimality criterion is suggested based on the concept of directional stiffness.First,under each single-load case(SLC),the truss-like structure is optimized as per the fully stressed criterion.Accordingly,the directional stiffness of the optimal structure under an SLC at every node is obtained.Next,the directional stiffness of the truss-like structure under MLCs is determined by ensuring that the directional stiffness is as similar as possible to the maximum directional stiffness of the optimal structure under every SLC along all directions.Finally,the directions and densities of the members in the optimal truss-like structures under MLCs are obtained by solving the eigenvalue problems of the coefficient matrix of the directional stiffness at every node.Two examples are presented to demonstrate the effectiveness and efficiency of the method.

A NEW STATISTICAL APPROACH FOR THE ANALYSIS OF UNCERTAIN SYSTEMS

This paper addresses the issues of conservativeness and computational complexity of probabilistie robustness analysis. The authors solve both issues by defining a new sampling strategy and robustness measure. The new measure is shown to be much less conservative than the existing one. The new sampling strategy enables the definition of efficient hierarchical sample reuse algorithms that reduce significantly the computational complexity and make it independent of the dimension of the uncertainty space. Moreover, the authors show that there exists a one to one correspondence between the new and the existing robustness measures and provide a computationally simple algorithm to derive one from the other.

Topology Optimization of Perforated Continua Based on Truss-Like Material Model

A topology optimization method from truss-like continua to perforated continua is studied, which is based on the concept of force transmission paths. The force transmission paths are optimized utilizing a truss-like material model. In the optimization procedure, parts of the force transmission paths are removed. Finally, perforated optimal continua are formed by further optimizing the material distribution field. No intermediate densities are suppressed; therefore, no additional technique is involved and no numerical instabilities are created. Structural topologies are presented using material distribution fields rather than the ＇existence＇ or ＇inexistence＇ of elements. More detailed structures are obtained utilizing less dense elements.