Uncertainty analysis in solid mechanics with uniform and triangular distributions using stochastic perturbation-based Finite 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.

Download Full-text

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

Computational Mechanics–New Frontiers for the New Millennium ◽

10.1016/b978-0-08-043981-5.50015-8 ◽

2001 ◽

pp. 65-70

Author(s):

Bo-nan Jiang

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Least Squares ◽

Solid Mechanics ◽

Element Method

Download Full-text

A Four-Noded Triangular (Tr4) Element for Solid Mechanics Problems with Curved Boundaries

International Journal of Computational Methods ◽

10.1142/s0219876218440036 ◽

2019 ◽

Vol 17 (01) ◽

pp. 1844003 ◽

Cited By ~ 1

Author(s):

Jun Hong Yue ◽

Guirong Liu ◽

Ruiping Niu ◽

Ming Li

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Solid Mechanics ◽

Accurate Approximation ◽

Shape Functions ◽

Curved Boundaries ◽

Triangular Elements ◽

Complicated Geometry ◽

Element Method ◽

Physics Problems

Linear triangular elements with three nodes (Tr3) were the earliest, simplest and most widely used in finite element (FE) developed for solving mechanics and other physics problems. The most important advantages of the Tr3 elements are the simplicity, ease in generation, and excellent adaptation to any complicated geometry with straight boundaries. However, it cannot model well the geometries with curved boundaries, which is known as one of the major drawbacks. In this paper, a four-noded triangular (Tr4) element with one curved edge is first used to model the curved boundaries. Two types of shape functions of Tr4 elements have been presented, which can be applied to finite element method (FEM) models based on the isoparametric formulation. FE meshes can be created with mixed linear Tr3 and the proposed Tr4 (Tr3-4) elements, with Tr3 elements for interior and Tr4 elements for the curved boundaries. Compared to the pure FEM-Tr3, the FEM-Tr3-4 can significantly improve the accuracy of the solutions on the curved boundaries because of accurate approximation of the curved boundaries. Several solid mechanics problems are conducted, which validate the effectiveness of FEM models using mixed Tr3-4 meshes.

Download Full-text

Coupled Analysis of Structural–Acoustic Problems Using the Cell-Based Smoothed Three-Node Mindlin Plate Element

International Journal of Computational Methods ◽

10.1142/s0219876216400077 ◽

2016 ◽

Vol 13 (02) ◽

pp. 1640007 ◽

Cited By ~ 11

Author(s):

Z. X. Gong ◽

Y. B. Chai ◽

W. Li

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Solid Mechanics ◽

Mindlin Plate ◽

Coupled Analysis ◽

Plate Element ◽

Fem Model ◽

The Face ◽

Smoothed Finite Element Method ◽

Element Method

The cell-based smoothed finite element method (CS-FEM) using the original three-node Mindlin plate element (MIN3) has recently established competitive advantages for analysis of solid mechanics problems. The three-node configuration of the MIN3 is achieved from the initial, complete quadratic deflection via ‘continuous’ shear edge constraints. In this paper, the proposed CS-FEM-MIN3 is firstly combined with the face-based smoothed finite element method (FS-FEM) to extend the range of application to analyze acoustic fluid–structure interaction problems. As both the CS-FEM and FS-FEM are based on the linear equations, the coupled method is only effective for linear problems. The cell-based smoothed operations are implemented over the two-dimensional (2D) structure domain discretized by triangular elements, while the face-based operations are implemented over the three-dimensional (3D) fluid domain discretized by tetrahedral elements. The gradient smoothing technique can properly soften the stiffness which is overly stiff in the standard FEM model. As a result, the solution accuracy of the coupled system can be significantly improved. Several superior properties of the coupled CS-FEM-MIN3/FS-FEM model are illustrated through a number of numerical examples.

Download Full-text