Research On Three-Dimensional Structural Topology Optimization Approach Based On Bone Remodeling Theory

Due to the development of technology,structural optimization is becoming more and more important.Finding the best solution in structure design within the existence constraint has always been the aim of engineers.Since the optimization theory provides an effective tool for solving the problem in the industry,the study on this subject makes potential contributions to the progress of structural optimization.There has been a growing interest in topology optimization.Topology optimization method could generate more economic advantages than shape and sizing optimization methods.However,because of the difficulties in topology description and problem solving, there are a lot of challenges in topology optimization study especially in continuum structural, such as mathematical modeling,the huge number of design variables,and the high cost of solving the problem.In this work,the continuum structure is studied.Based on the bone remodeling theories,strain energy density dead zone conception and the fabric tensor theory,a floating interval of reference strain energy density approach is proposed.This method provides a floating interval of strain energy density to control the update of design variables.Three-dimensional continuum structural topology optimization analysis method is proposed to find the minimum weight,with the constraints of volume and displacement.The numerical examples in this paper show the feasibility of this method.The major idea of the present method is to consider the structure as a piece of bone.In this way,it can be remodeled follows the Wolff's law.The growing process is controlled by a floating interval of reference strain energy density;in another word,in a point of the domain, increasing or removing the material is decided by the comparison between the strain energy density and the floating interval of reference.As the 'bone' reaches the equilibrium state of remodeling,the final optimal structure is obtained.Wolff's law means bone microstructure and local stiffness tend to align with the stress principal directions to adapt to the mechanical environments.The research work of the dissertation is supported by the National Natural Science Foundation of China(10721062),the National Key Basic Research Special Foundation of China(2005CB321704) and the New Century Educational Talents Plan of Chinese Education Ministry,China(under contract No.NCET-07-0128).