Least-Squares Finite Element Method for Computational Fluid and Solid Mechanics

2001 ◽  
pp. 65-70
Author(s):  
Bo-nan Jiang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Least Squares ◽  
Solid Mechanics ◽  
Element Method

Topology Optimization Using Node-Based Smoothed Finite Element Method

2015 ◽  
Vol 07 (06) ◽  
pp. 1550085 ◽  
Author(s):  
Z. C. He ◽  
G. Y. Zhang ◽  
L. Deng ◽  
Eric Li ◽  
G. R. Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Topology Optimization ◽  
Optimization Design ◽  
Solid Mechanics ◽  
Optimality Criteria ◽  
Topology Optimization Problem ◽  
Design Variables ◽  
Smoothed Finite Element Method ◽  
Element Method

The node-based smoothed finite element method (NS-FEM) proposed recently has shown very good properties in solid mechanics, such as providing much better gradient solutions. In this paper, the topology optimization design of the continuum structures under static load is formulated on the basis of NS-FEM. As the node-based smoothing domain is the sub-unit of assembling stiffness matrix in the NS-FEM, the relative density of node-based smoothing domains serves as design variables. In this formulation, the compliance minimization is considered as an objective function, and the topology optimization model is developed using the solid isotropic material with penalization (SIMP) interpolation scheme. The topology optimization problem is then solved by the optimality criteria (OC) method. Finally, the feasibility and efficiency of the proposed method are illustrated with both 2D and 3D examples that are widely used in the topology optimization design.

scholarly journals Interval study of convergence in the solution of 1D Burgers by least squares finite element method (LSFEM) + Newton linearization

2015 ◽  
Vol 10 (16) ◽  
pp. 522-530 ◽  
Author(s):  
Fernanda Soares de Oliveira e Silva Barbara ◽  
Veloso Garcia Roberta ◽  
Cristiane Pinto Mesquita Pardal Paula ◽  
Claro Romao Estaner
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Least Squares ◽  
Element Method
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