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中文摘要：
基于生物力学中的Wolff法则，发展了一种连续体拓扑优化的新方法。有待优化的结构被看作是一块遵从Wolff法则生长的骨骼，把寻找其最优拓扑的过程比拟为骨骼的重建／生长过程，采用骨骼的重建／生长规律作为准则更新材料分布，直至达到一个平衡状态并由此获得结构的最优拓扑。算例表明了所提出方法的有效性。
英文摘要：
Wolff＇s law in biomechanics states that the bone continually adapts to its mechanical environment through cell-based remodeling of trabecular surfaces and the local microstructure tends to align with the principal directions of the stress. The objective of the present research is to develop a new rule-based method for continuum topology optimization based on Wolff＇s law. The major ideas of the present approach are as follows. Firstly, the structure is to be optimized as a piece of bone which obeys Wolff＇s law. Secondly, the process of finding the optimal structural topology is equivalent to the ＂bone＂ remodeling/growth process. Thirdly, the remodeling rule can be explained as follows： During the process of growth, at any material point in the structure, if the absolute value of one of its principal strains is out of a given interval of reference strain, then the material in the local microstructure along the corresponding direction should be adjusted. If the absolute values of all its principal strains locate in the interval, the material point is in a state of equilibrium of remodeling. Finally, the global optimization of structure requires all material points to be in the state of remodeling equilibrium under the loading conditions. In order to express the microstructure and the anisotropic behavior of a material point, a second rank positive and definite fabric tensor is introduced. The relative density of a point in design domain expressed by the invariants of the fabric tensor through the mathematical condensation of the porous medium based on the stiffness-equivalence rule is used to display the optimal topology of structure. Examples are given to show the validity and capability of the proposed approach for the optimal topology design of continuum structures.
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