Generating optimal topologies in structural design using a homogenization method
Computer Methods in Applied Mechanics and Engineering
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A grid generation and flow solution method for the Euler equations on unstructured grids
Journal of Computational Physics
The fast construction of extension velocities in level set methods
Journal of Computational Physics
Structural boundary design via level set and immersed interface methods
Journal of Computational Physics
Structural optimization using sensitivity analysis and a level-set method
Journal of Computational Physics
Mesh generation for implicit geometries
Mesh generation for implicit geometries
Velocity Extension for the Level-set Method and Multiple Eigenvalues in Shape Optimization
SIAM Journal on Control and Optimization
Topological shape optimization of geometrically nonlinear structures using level set method
Computers and Structures
An isoparametric approach to level set topology optimization using a body-fitted finite-element mesh
Computers and Structures
Stress-based topology optimization using an isoparametric level set method
Finite Elements in Analysis and Design
Structural and Multidisciplinary Optimization
A mesh evolution algorithm based on the level set method for geometry and topology optimization
Structural and Multidisciplinary Optimization
Level-set methods for structural topology optimization: a review
Structural and Multidisciplinary Optimization
A survey of structural and multidisciplinary continuum topology optimization: post 2000
Structural and Multidisciplinary Optimization
Topology optimization using an explicit interface representation
Structural and Multidisciplinary Optimization
Hi-index | 0.00 |
Using hyperelastic materials and unstructured mesh, a level set based topological shape optimization method is developed for geometrically nonlinear structures in total Lagrangian framework. In the level set method, the initial domain is kept fixed and its boundary is represented by an implicit moving boundary embedded in a level set function, which facilitates to handle complicated topological shape changes and eventually leads the initial implicit boundary to an optimal one according to the normal velocity field while both minimizing the objective function of instantaneous structural compliance and satisfying an allowable material volume constraint. In existing level set based methods, an initial reference domain or an ersatz material is employed for the penalization of whole domain to represent the current domain. However, these approaches end up with a convergence difficulty in nonlinear response analysis due to the inaccurate tangent stiffness. To overcome this difficulty, taking advantage of the obtained level set function, the current structural boundary is actually represented using a Delaunay triangulation scheme and a hyperelastic material law is employed to handle the large strain problem. The required velocity field in the actual domain to update the level set equation is determined from the descent direction of Lagrangian derived from optimality conditions. The velocity field outside the actual domain is determined through a velocity extension scheme based on a fast marching method. Since homogeneous material property and actual boundary are utilized, the convergence difficulty is significantly relieved.