Isogeometric material density field structure topology optimization method
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A material density and topology optimization technology, applied in design optimization/simulation, instrumentation, calculation, etc., can solve problems such as checkerboard problems, non-smooth local minima, and achieve efficiency improvement, error elimination, and adaptability
Active Publication Date: 2019-04-23
HUAZHONG UNIV OF SCI & TECH
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Therefore, in the final optimization results, such as: checkerboard pro...
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example 1
[0073] Example 1, please refer to Figure 2~4
[0074] (1) if figure 2 As shown, the design domain is a cantilever beam structure with L=10, H=5, the left boundary is fixed, and there is a concentrated load F=1 at the middle point of the right boundary.
[0075] (2) Define the parameters as follows: target volume 30%, penalty factor 3, polynomial exponent of NURBS basis function 3, isogeometric analysis grid contains 100×50 elements, two parameter directions ξ, node vectors on η respectively For: Ξ={0, 0, 0, 0, 0.01, ..., 0.99, 1, 1, 1, 1} and The numbers of control vertices on the parameter directions ξ and η are respectively n=103 and m=53.
[0076] (3) Use the Shepard function to smooth the control vertex density, and the smoothed control vertex density can be expressed as:
[0077]
[0078] In the formula, is the smoothed density of control vertex (i, j), ρ i，j Indicates the density at the control vertex (i, j), w(ρ i，j) represents the weight at the control ve...
example 2
[0104] Instance 2, please refer to Figure 5-7
[0105] Figure 5 Take a 1 / 4 ring structure with an outer diameter of R=10 and an inner diameter of r=5 as an example. It is fixed at the vertex of the upper left corner, and a downward force F=1 is applied, and the lower right edge is slidably fixed. The degree of the NURBS basis function is 3. The node vectors of the two parameter directions are: Ξ={0, 0, 0, 0, 0.01, ..., 0.99, 1, 1, 1, 1} and The corresponding isogeometric grid contains 100×50 cells. The number of control points in the two parameter directions is 103×53, the number of design variables is 5459, and the maximum target volume fraction V 0 40%. The total compliance value obtained by final optimization is 110.39.
[0106] The optimization process of Example 2 is the same as that of Example 1. Figure 6 In order to optimize the results, it is not difficult to see that the optimization of the curve boundary also has a good effect, Figure 7 is the iterativ...
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Abstract
The invention belongs to the technical field of structure optimization, and discloses an isogeometric material density field structure topology optimization method. The method comprises the steps of (a) giving a design domain to serve as an object to be optimized, and constructing an NURBS curved surface corresponding to the design domain; (b) calculating an isogeometric material density distribution field of the NURBS curved surface, establishing a structural optimization design model of a design domain, enabling the design domain to still meet the structural rigidity performance requirementwhile the size is reduced, and defining the design model to obtain the density corresponding to each control vertex in the design domain; and (c) establishing an optimization criterion to update the density and converge the density so as to obtain the density corresponding to each point in the required design domain, thereby realizing the topological optimization of the isogeometric material density field structure. By means of the topological optimization method, the structural optimization design is effectively achieved, the common chessboard problem, grid dependence, the island phenomenon and other numerical instability problems in topological optimization design are eliminated, the topological optimization structure is smoother, and the optimization solving efficiency is improved.
Description
technical field [0001] The invention belongs to the technical field of structure optimization, and more specifically relates to a method for topology optimization of an equigeometric material density field structure. Background technique [0002] The Variable Density Method (SIMP) is one of the commonly used methods in topology optimization. Its characteristic is to convert discrete design variables into continuous variables by using an isotropic material interpolation model. The method relies heavily on artificial parameters to remove numerical instabilities, and there are no reasonable guidelines until optimal parameters are determined. [0003] The Bidirectional Asymptotic Structural Optimization (BESO) method allows simultaneous removal and addition of material at each iterative step in the optimization process. The sensitivity number of the empty element is obtained by the linear estimation of the displacement field obtained by the finite element analysis. Then, the so...
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