Research on Ratio-Extremum Algorithm for Topology Optimization of Continuum Structures Including Active Constraint Identification
Ou Disheng,
Zheng Xuefen,
Zhou Xiongxin
Issue:
Volume 10, Issue 1, February 2022
Pages:
1-6
Received:
16 January 2022
Accepted:
29 January 2022
Published:
16 February 2022
Abstract: To obtain the topology optimization algorithm of continuum structure which can effectively identify the effective constraints and quickly converge, based on the original Ratio-Extremum algorithm theory based on truss structure optimization, the emitter algorithm theory is introduced into the topology optimization of continuum structure. Firstly, taking pseudo density as design variables, mathematical model of the minimization mass with constraints of nodal displacements and element stresses is constructed. Secondly, according to essential extremum conditions of Dual objective function, iterative optimization direction and analytical step-size of constraint multipliers are derived. And, according to essential extremum conditions of Generalized Lagrange function, iterative optimization direction and analytical step-size of pseudo densities are derived. Analytical step-sizes are used to avoid one-dimensional optimization and then the calculation quantity of iterative optimization can be decreased. Thirdly, first-order partial derivatives of nodal displacement and element equivalent stress constraints with respect to pseudo densities are given. After that, by using self-compiled MATLAB program for continuum structure analysis, partial derivative calculation and optimization iteration, 4 optimization examples of different beam structures are used to show the changes of active nodal displacement and element equivalent stress constraints, and structural mass in the optimization iteration process, and to show the effectiveness of Ratio-Extremum algorithm in topology optimization of continuum structures.
Abstract: To obtain the topology optimization algorithm of continuum structure which can effectively identify the effective constraints and quickly converge, based on the original Ratio-Extremum algorithm theory based on truss structure optimization, the emitter algorithm theory is introduced into the topology optimization of continuum structure. Firstly, ta...
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Development of New Sound Insulation Simulation Technology Using Finite Element Method for Efficiency of High Aspect Ratio Core in Low Frequency Range
Issue:
Volume 10, Issue 1, February 2022
Pages:
7-16
Received:
18 February 2022
Accepted:
11 March 2022
Published:
18 March 2022
Abstract: Nowadays, meta-materials are being studied to reduce vehicle interior noise. But it has not yet been found effective meta-materials at low frequencies below 500Hz. A panel with one core which has an excellent sound insulation where the higher the height of the core, the better the sound insulation characteristics have been founded. And so, depending on the core height, a structure with one core which is effective even at 500hz or less may be obtained. If the core height is high, it cannot be obtained by press forming, so the origami forming has been developed. Use of FEM which is versatile for shape of structure is effective for analysis of the plate with core or with sound absorbing material. Although the FEM analysis for sound insulation analysis was difficult, so far, two methods have been developed. Here these two methods to a flat plate and a flat plate with sound absorbing material to grasp their characteristics are compared and applied. And then the more versatile method is selected for sound insulation analysis to plates with one core which are formed by origami forming. As a result, it is shown that a plate with one core is effective for sound insulation characteristics at the low frequency below 500Hz depending on the balance between plate thickness and core height. At last, it is shown the core shape that maximizes the integral value of the sound insulation characteristic from 0 Hz to 500 Hz by an optimal analysis.
Abstract: Nowadays, meta-materials are being studied to reduce vehicle interior noise. But it has not yet been found effective meta-materials at low frequencies below 500Hz. A panel with one core which has an excellent sound insulation where the higher the height of the core, the better the sound insulation characteristics have been founded. And so, dependin...
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