On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix. Part 1: Theory

1990 ◽  
Vol 11 (5) ◽  
pp. 587-620 ◽  
Author(s):  
Philip M. Gresho
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Incompressible Flow ◽  
Mass Matrix ◽  
Projection Methods ◽  
Viscous Incompressible Flow ◽  
Consistent Mass Matrix ◽  
Element Method

Lumped Mass Matrix of Three-Node Beam Element

2012 ◽  
Vol 616-618 ◽  
pp. 1969-1973 ◽  
Author(s):  
Lv Zhou Ma ◽  
Jian Liu ◽  
Xiao Dong Jia ◽  
Yu Qin Yan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Kinetic Energy ◽  
Mass Matrix ◽  
Beam Element ◽  
Diagonal Matrix ◽  
Lumped Mass ◽  
Consistent Mass Matrix ◽  
Element Method

According to Hamilton theory and the concept of Kinetic energy, lumped mass matrix of three-node beam element based on positional finite element method (FEM) is deduced. By concentrating the mass at the three nodes of beam element, the lumped mass matrix is characterized. When dynamic analysing, lumped mass matrix is simpler and more common than consistent mass matrix because lumped mass matrix is diagonal matrix, and calculation work is less under the same calculation precision.

Nonlinear Random Responses of Shell Structures With Spatial Uncertainties

2002 ◽  
Author(s):  
C. W. S. To
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Large Deformation ◽  
Mass Matrix ◽  
Spatial Uncertainty ◽  
Shell Structures ◽  
Time Step ◽  
Central Difference ◽  
Approximation Techniques ◽  
Element Method

A novel procedure for large deformation nonstationary random response computation of shell structures with spatial uncertainty is presented. The procedure is free from the limitations associated with those employing perturbation approximation techniques, such as the so-called stochastic finite element method and probabilistic finite element method, for systems with spatial uncertainties. In addition, the procedure has several important and excellent features. Chief among these are: (a) ability to deal with large deformation problems of finite strain and finite rotation; (b) application of explicit linear and nonlinear element stiffness matrices, mass matrix, and load vectors reduces computation time drastically; (c) application of the averaged deterministic central difference scheme for the updating of co-ordinates and element matrices at every time step makes it extremely efficient compared with those employing the Monte Carlo simulation and the conventional central difference algorithm; and (d) application of the time co-ordinate transformation enables one to study highly stiff structural systems.

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