Topology Optimization Of Truss-like Structures Under Uncertain Load By Eigenvalue Method

The loads applied to the engineering structures will be affected by many factors,such as construction error,measurement error,temperature change and other environmental factors.Under the influence of these environmental factors,it is difficult to ensure that the loads are deterministic.When these uncertain loads are applied to the structures,their reliabilities and safeties will be reduced.Therefore,it is great significant to improve the structural reliabilities and safeties to study the topology optimization method under uncertain loads.Generally,probability-based method and non-probability-based method are adopted to solve the structure topology optimization.When the probability information of uncertain parameters is unavailable,the non-probability-based method is suitable to be applied.In this paper the non-probability-based method is adopted.Firstly,the two-bars structure with anisotropy in tension and compression acted by certain loads and uncertain loads are optimized by analytical method.Under the uncertain load,which direction can vary arbitrarily or in the given range of the interval;the structural compliance is minimized with volume constrained and the structural volume is minimized with stress constrained,respectively.The topology optimization of truss-like continuum structure under uncertain load is analyzed.Based on the convex set model,the load with uncertain is divided into two parts: the average value and the error.The average value is deterministic,and the error is changeable.The structural response is also divided into two parts by these two loads.The load in worst case is obtained by the eigenvalue method.Then the topology optimization method based on the truss-like material model is applied to optimize the structure.This procedure is repeated until the change in two consecutive iterations is little enough.Finally,the topology optimization structure under the uncertain load is obtained.It is showed that the difference between optimal topology of truss-like structure acted by the uncertain loads and that acted by the certain loads.Therefore,it is more reasonable and safer to consider the uncertainty of loads in the actual engineering structure.In the process of iterative calculation,eigenvalue method has more obvious efficiency.Based on the truss-like material model,without deleting elements and suppressing the intermediate density,there are no instability phenomena such as element dependence,checkerboard and elements jointed at their corner nodes.Finally,several structures commonly used in practical engineering are analyzed...