For the sensitivity analysis, a particle-based discrete adjoint methodology for the level set topology optimization method is presented. The applicability of the methodology is illustrated through examples and compared with the literature.

For the optimization, the simplified case of steady-state FSI is assumed. TheĬoupling of the different methods is illustrated through the analysis of transient FSI examples. 2001 Zong, 2003), and meshfree methods based on the weak forms (or short. To accomplish this, the LSTO-RKPM methodology is further combined with the modified immersed finite element method (mIFEM). Numerical examples of two-dimensional solids are presented to demonstrate the. The development of the LSTO-RKPM methodology is later extended to fluidstructure interactions. Different integration schemes, particle distributions and continuity orders are also explored to pin down the best balance Several review papers and books have been published on meshfree methods Belytschko et al. The methodology is first validated for purely hydrostatic pressure, which is a very simple case of design-dependent physics. meshfree methods, in order to exploit of the advantages of each method (see Belytschko et al., 1995 Hegen, 1996 Liu et al., 1997b Huerta and Fern andez-M endez, 2000 Hao et al., 2004). In this way, the difficulties associated with fixed grid LSTO methods and remeshing-based approaches are avoided. In this thesis a meshfree level set topology optimization methodology based on the reproducing kernel particle method (RKPM) is developed toĮnsure the well-defined geometrical representation of the structural boundary is transferred onto the computational domain by placing RKPM particles along the boundary. On the other hand, remeshing the structure at each iteration directly addresses the problem, it posesĪdditional difficulties because of the need to ensure good quality meshes at each iteration. However, maintaining this crisp boundary representation onto the computational model for the analysis is not straightforward especially with fixed grid methodologies. Optimization (LSTO) possesses an advantage over traditional density-based methods since it provides clearly defined boundaries. In the last decade, the development of the RBFs method as a truly meshfree. Fluid-structure interaction (FSI) is a typical example. RBFs are used actively for solving PDEs, and the examples can be found in 10-14.

This is a challenging class of problems governed by interface conditions and loadings. The finite difference method (FDM) hasbeen used tosolve differential equation systems for centuries. This thesis aims to develop computational tools for multiphysics problems in topology optimization with particular focus on design-dependent surface physics. characterisations, examples Conditionally positive definite functions. Copyright © 2006 by ASME.PDF (Electronic Thesis and Dissertation Publication Form) Meshfree methods are a modern tool for the reconstruction of an unknown function. Numerical examples are presented to illustrate the computational efficiency and accuracy of the proposed method. The proposed enriched basis function can be viewed as a generalized enriched basis function, which degenerates to a linear-elastic basis function when the bimaterial constant is zero. The IMLS has higher computational efficiency and precision than the MLS, and will not lead to an ill-conditioned system of equations. In the IMLS method, the orthogonal function system with a weight function is used as the basis function. The method involves an element-free Galerkin formulation in conjunction with IMLS and a new enriched basis functions to capture the singularity field in linear-elastic bi-material fracture mechanics. This paper presents an enriched meshless method based on an improved moving least-square approximation (IMLS) method for fracture analysis of cracks in homogeneous, isotropic, linear-elastic, two-dimensional bimaterial solids, subject to mixed-mode loading conditions.

Meshfree method examples