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Register a new userTopology optimization of nonlinear periodically microstructured materials for tailored homogenized constitutive properties
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Added by
Reza Behrou
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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A topology optimization method is presented for the design of periodic microstructured materials with prescribed homogenized nonlinear constitutive properties over finite strain ranges. The mechanical model assumes linear elastic isotropic materials, geometric nonlinearity at finite strain, and a quasi-static response. The optimization problem is solved by a nonlinear programming method and the sensitivities computed via the adjoint method. Two-dimensional structures identified using this optimization method are additively manufactured and their uniaxial tensile strain response compared with the numerically predicted behavior. The optimization approach herein enables the design and development of lattice-like materials with prescribed nonlinear effective properties, for use in myriad potential applications, ranging from stress wave and vibration mitigation to soft robotics.
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This paper presents an efficient gradient projection-based method for structural topological optimization problems characterized by a nonlinear objective function which is minimized over a feasible region defined by bilateral bounds and a single linear equality constraint. The specialty of the constraints type, as well as heuristic engineering experiences are exploited to improve the scaling scheme, projection, and searching step. In detail, gradient clipping and a modified projection of searching direction under certain condition are utilized to facilitate the efficiency of the proposed method. Besides, an analytical solution is proposed to approximate this projection with negligible computation and memory costs. Furthermore, the calculation of searching steps is largely simplified. Benchmark problems, including the MBB, the force inverter mechanism, and the 3D cantilever beam are used to validate the effectiveness of the method. The proposed method is implemented in MATLAB which is open-sourced for educational usage.
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This paper presents an analytic model of one dimensional magnetostriction. We show how specific assumptions regarding the symmetry of key micromagnetic energies (magnetocrystalline, magnetoelastic, and Zeeman) reduce a general three-dimensional statistical mechanics model to a one-dimensional form with an exact solution. We additionally provide a useful form of the analytic equations to help ensure numerical accuracy. Numerical results show that the model maintains accuracy over a large range of applied magnetic fields and stress conditions extending well outside those produced in standard laboratory conditions. A comparison to experimental data is performed for several magnetostrictive materials. The model is shown to accurately predict the behavior of Terfenol-D, while two compositions of Galfenol are modeled with varying accuracy. To conclude we discuss what conditions facilitate the description of materials with cubic crystalline anisotropy as transversely isotropic, to achieve peak model performance.
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