7-2 The Constant Strain Triangle (CST ) An element of triangular shape is easy to develop and can be used to model irregular boundaries. The three node triangular element was one of the first elements extensively used for continuum stress analysis.
In mechanics, strain is defined as relative deformation, compared to a reference position configuration. Different equivalent choices may be made for the expression of a strain field depending on whether it is defined with respect to the initial or the final configuration of the body and on whether the metric tensor or its dual is considered.
8.5.1 Constant strain triangle element. The constant strain triangle (CST) is one of the earliest elements developed [1]. Use of this element in solid mechanics problems has certain drawbacks. This element does not represent bending properly and is prone to predict spurious shear strains.
To derive the constant-strain triangle (CST) element stiffness matrix and equations. To demonstrate how to determine the stiffness matrix and stresses for a constant strain element. To describe how to treat body and surface forces for two-dimensional elements. To evaluate the explicit stiffness matrix for the constant-strain triangle element.
Constant Strain Triangle • Recall the shape funcJons used to interpolate the nodal displacements in 1D problems. Here in 2D problems we determine the displacements inside an element from the 3 nodal displacements using linear shape funcJons. • By inspecJon we see that N 1 +N 2 +N 3 =1. This means that they are not linearly independent.
Previously we developed the FEA mathematics for a constant strain triangular mesh. This method is applicable to problems that can be idealized as two dimensional plates. All constraints and loads must be in the plane of the plate. (4.74) for computing the …
Constant strain triangle (CST) is the simplest element to develop mathematically. In CST, strain inside the element has no variation (Ref. module 3, lecture 2) and hence element size should be small enough to obtain accurate results.
CONSTANT STRAIN FINITE ELEMENTS FOR ISOCHORIC STRAIN FIELDS John H. Argyris and Padraic C. Dunne Institut for Statik und Dynamik (University of Stuttgart) 1. Introduction As the finite element method is increasingly finding application in non-linear problems it is clear that the simpler finite elements are coming back into favour.