Applied element method: Difference between revisions

Revision as of 11:07, 20 October 2011

Revision as of 01:38, 6 July 2012

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===Element generation and formulation===

The modeling of objects in AEM is very similar to modeling objects in [[Finite element method|FEM]]. Each object is divided into a series of elements connected together and forming a mesh. The main difference between AEM and FEM, however, is how the elements are joined together. In AEM the elements are connected by a series of [[Nonlinear system|non-linear]] springs representing the material behavior.

There are three types of springs used in AEM:

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Although the element motion moves as a [[rigid body]], its internal [[Deformation (engineering)|deformations]] are represented by the spring deformation around each element. This means the element shape does not change during analysis, but the behavior of assembly of elements is deformable.

The two elements are assumed to be connected by only one pair of normal and shear springs. To have a general stiffness matrix, the locations of element and contact springs are assumed in a general position. The stiffness matrix components corresponding to each [[Degrees of freedom (physics and chemistry)|degree of freedom]] are determined by assuming a unit [[Displacement (vector)|displacement]] in the studied direction and by determining forces at the [[centroid]] of each element. The 2D element stiffness matrix size is 6 x× 6; the components of the upper left quarter of the [[stiffness matrix]] are shown below:

: <math>\begin{bmatrix}