scholarly journals Treatment of Nonlinear Multi Freedom Boundary Constraints in Finite Element Analysis of Frame System using Lagrange Multiplier Method

2020 ◽  
Vol 960 ◽  
pp. 022076
Author(s):  
Vu Thi Bich Quyen ◽  
Dao Ngoc Tien ◽  
Nguyen Thi Lan Huong
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Lagrange Multiplier ◽  
Lagrange Multiplier Method ◽  
Multiplier Method ◽  
Element Analysis ◽  
Boundary Constraints ◽  
Frame System

The Equivalence Proof of Two Methods for Foundation Excitation

2014 ◽  
Vol 638-640 ◽  
pp. 684-689
Author(s):  
Yun Ying Ma ◽  
Jin Duan ◽  
Hong Shao
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Lagrange Multiplier ◽  
Present Theory ◽  
Degree Of Freedom ◽  
Multiplier Method ◽  
Element Analysis ◽  
Numerical Example ◽  
The Finite Element Analysis ◽  
Equivalence Proof

In this paper, the two methods for the finite element analysis of foundation excitation would be proved mathematically equivalent. Although the two methods, i.e. the method of degree-of-freedom transformation and the Lagrange multiplier method, are absolutely different in appearance, but their mathematical essence would be proved completely identical. In other words, although the equations derived from the two methods have different degree-of-freedoms, i.e. the latter much more than the former, while in essence they could be deduced from each other and vice versa. And finally a numerical example will be presented and discussed to demonstrate the correctness of the present theory.

On the finite element analysis of contacting bodies using submodelling

2005 ◽  
Vol 40 (2) ◽  
pp. 95-106 ◽  
Author(s):  
R Rajasekaran ◽  
D Nowell
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Contact Problem ◽  
Lagrange Multiplier ◽  
Analytical Approach ◽  
Partial Slip ◽  
Element Analysis ◽  
Penalty Formulation ◽  
Lagrange Formulation ◽  
The Finite Element Analysis

The implication of selecting different contact algorithms in solving a contact problem by a submodelling approach is highlighted using the example of a partial slip Cattaneo-Mindlin problem. It is shown that, by employing a penalty formulation, the state of partial slip can be incorrectly predicted as full sliding whereas a Lagrange formulation predicts the correct slip-stick behaviour. The displacements along the centre-line of contact are calculated by analytical approach and compared with finite element results. It is found that the Lagrange multiplier approach predictions match the analytical results well, but prediction by the penalty formulation is sensitive to the slip tolerance selected. It is concluded that care should be exercised while using the penalty formulation for displacement-controlled problems.

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