Variational multiscale analysis of elastoplastic deformation using meshfree approximation

AbstractA variational multiscale method has been presented for efficient analysis of elastoplastic deformation problems. Severe deformation occurs in plastic region and leads to high gradient displacement. Therefore, solution needs to be refined to properly capture local deformation in plastic region. In this work, scale decomposition based on variational formulation is presented. A coarse scale and a fine scale are introduced to represent global and local behavior, respectively. The displacement is decomposed into a coarse and a fine scale. Subsequently the problem is also decomposed into a coarse and a fine scale from the variational formulation. Each scale variable is approximated using meshfree method. Adaptivity can easily and nicely be implemented in meshfree method. As a method of increasing resolution, extrinsic enrichment of partition of unity is used. Each scale problem is solved iteratively and conversed results are obtained consequently. Iteration procedure is indispensable for the elastoplastic deformation analysis. Therefore iterative solution procedure of each scale problem is naturally adequate. The proposed method is applied to the Prandtl’s punch test and shear band problem. The results are compared with those of other methods and the validity of the proposed method is demonstrated

Thermo-viscoplastic analysis of hypersonic structures subjected to severe aerodynamic heating

A thermoviscoplastic computational method for hypersonic structures is presented. The method employs unified viscoplastic constitutive model implemented in a finite element approach for quasi-static thermal-structural analysis. Applications of the approach to convectively cooled hypersonic structures illustrate the effectiveness of the approach and provide insight into the transient inelastic structural behavior at elevated temperatures

Globally Convergent Topology Optimization using Level Set Method

Main objective of this research is to develop and implement a numerical procedure to guarantee global convergence of the level set based topology optimization method. To verify the proposed topology optimization procedure, several numerical examples are treated. From the results of verification process, the hole creation and the global convergence are examined. In the optimization process, two dimensional elastic structure is considered. The objective function is selected as the compliance of a structure. As a constraint, the total volume (or mass) of a structure is limited to be a certain value. The sensitivities of the objective function and the constraint are calculated by direct di#erentiation method. Using the finite element analysis, performances of the optimized results are analyzed

The Design of Reflective Mirrors for High-power Laser Systems using Topology Optimization

Recently high-power laser has been developed for various applications. High energy absorbed by reflective mirrors through high-power laser beam might distort the reflective mirror surfaces and degrade system performance. However, high-power laser system must be capable of transporting and directing the beam with high accuracy. Thus it is important to minimize the distortion. For the optimal optical performance of the mirror with least possible weight, topology optimization method is applied. To investigate the distortion of mirror surface by the high-power laser, thermo-elastic analysis is performed with three dimensional models. Thermal analysis considering conduction and convection is performed. In this analysis, heat source by the high power laser is treated as the heat flux on the mirror front surfaces. Through the obtained thermal distribution, deformation and distortion of mirror surface are calculated. As a measure of thermal distortion on the mirror surface, root mean square(RMS) value of mirror surface is used. In the optimization procedure, RMS value is used as the objective function, and total mass of the reflective mirror is constrained to be a certain value. The sensitivities of the objective function and constraint are calculated by direct differentiation method. Optimization procedure is carried out by an optimality criteria method using the sensitivities of the objective function and the constraint. The proposed formulation and the design procedures are applied to the design of the mirror-backing surface in real high-power laser system