Topological optimization of continuum structures with design-dependent surface loading – Part II: algorithm and examples for 3D problems

  • J. Du
  • N. Olhoff
Research paper


The problem of topology optimization of 3D structures with design-dependent loading is considered. An algorithm for generating the valid loading surface of the 3D structure is presented, constituting an extension of the algorithm for 2D structures developed in Part I of this paper on the basis of a modified isoline technique. In this way the complicated calculation of the fit of the loading surface of a 3D structure may be avoided. Since the finite element mesh is fixed in the admissible 3D design domain during the period of topology evolution, the design-dependent loading surface may intersect the elements as the design changes. Independent interpolation functions are introduced along the loading surface so that the surface integral for generating the loading on the surface of the 3D structure can be performed more efficiently and simply. The bilinear 4-node serendipity surface element is constructed to describe the variable loading surface, and this matches well with the 8-node isoparametric 3D elements which have been used for the discretization of the 3D design domain. The validity of the algorithm is verified by numerical examples for 3D problems. Results of designing with design-dependent loads and with corresponding fixed loads are presented, and some important features of the computational results are discussed.


design-dependent loading serendipity surface element surface integral three dimensional (3D) structures loading surface topology design  


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© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Institute of Mechanical EngineeringAalborg UniversityAalborg EastDenmark

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