Abstract
The topology optimization method of continuum structures is adopted for the morphogenesis of dendriforms during the conceptual design phase. The topology optimization model with minimizing structural strain energy as objective and subject to structural weight constraint is established by the independent continuous mapping method (ICM) which is a popular and efficient method for the topology optimization of continuum structures. This optimization model is an optimization problem with a single constraint and can be solved by the iteration formula established based on the saddle condition. Taking the morphogenesis of a plane dendriform as an example, the influences on topologies of the dendriform are discussed for several factors such as the ratio of the reserved weight to the total weight, the stiffness and the geometry shape of the roof structure, the height of the design area, and so on. And several examples of application scenarios are presented, too. Numerical examples show that the proposed structural topology optimization method for the morphogenesis of dendriforms is feasible. It can provide diversiform topologies for the conceptual design of dendriforms.
Highlights
Dendriforms, which was put forward first by a German Frei Otto in the 1960s, is a kind of bionic structure designed based on the shapes and mechanical characteristics of natural trees
The topology optimization method of continuum structures is adopted for the morphogenesis of dendriforms during the conceptual design phase
1) It is showed from the numerical examples that it is feasible to generate dendriforms by the topology optimization method of continuum structures
Summary
Dendriforms, which was put forward first by a German Frei Otto in the 1960s, is a kind of bionic structure designed based on the shapes and mechanical characteristics of natural trees. Using the optimization method of skeleton structures, Changyu Cui proposed the form finding method of dendriforms based sensitivity [7]. He improved the evolutionary structural optimization method (ESO) method, which was a topology optimization method of continuum structures, to generate the optimal topology of dendriforms [8]. The more rational design can be achieved by the form finding method based on the topology optimization of continuum structures because the optimal topologies with skeleton forms can be obtained, and it is unnecessary to specify some prior data such as the height, the layers and the numbers of branches. Several application examples are presented to illustrate the feasibility of the proposed method
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