Structural & Continuum Elements

The finite element method involves modeling the structure using small interconnected elements called finite elements . Selecting the right element for an analysis is the key for obtaining physically correct simulation.

Isoparametric Formulation

In isoparametric formulation , same shape functions (or interpolation functions) are used to define the element’s geometric shape and the displacements within the element.

Isoparametric element equations are formulated using a natural coordinate system (ξ ,η) that is defined by element geometry and not by the element orientation in the global-coordinate system.

Mapping of the simple geometric shape in the local coordinate system into distorted shapes in the global cartesian coordinate system is achieved by shape function's .This relationship provides the required mapping from the local coordinate system to the global coordinate system and is known as isoparametric mapping.

Using isoparametric formulation , numerical integration of element matrices are performed in local (ξ ,η) co-ordinate frame and then transformed in to global coordinate frame.

Euler-Bernoulli Beam

A beam is a long, slender structural member generally subjected to transverse loading that produces bending effects.

Constant Strain Triangle

3 Node Triangle element is a 2D element with two degrees of freedom at each node i.e. translations in the nodal x and y directions.
It can be used as either a plane element (plane stress, plane strain) or an axisymmetric element.
The strain displacement matrix has constant terms and does not vary in ξ-η coordinate space , hence strain is constant in the element.

Bilinear Quadrilateral

4 Node Quadrilateral is a 2D element defined by four nodes with two degrees of freedom at each node i.e. translations in the nodal x and y directions.
It is bilinear because of the linear terms in x and y for the x and y displacement functions.
It can be used as either a plane element (plane stress, plane strain) or an axisymmetric element.
Standard element is based on pure displacement formulation which leads to shear and volumetric locking.
SCIFESOL provides Enhanced assumed strain (EAS) and B-Bar formulation to remove shear and volumetric locking in the element.

Quadratic Quadrilateral

8 Node Quadrilateral is a 2D element defined by eight nodes with two degrees of freedom at each node i.e. translations in the nodal x and y directions.
It can be used as either a plane element (plane stress, plane strain) or an axisymmetric element.
It has quadratic terms in x and y for the x and y displacement functions.
The element is part of serendipity family of elements.
It is free from shear locking phenomenon.

Tetrahedron

4 Node Tetrahedral is a 3D element defined by four nodes with three degrees of freedom at each node i.e. translations in the nodal x ,y and z directions.
The strain displacement matrix has constant terms and does not vary in natural coordinate space , hence strain is constant in the element.

Hexahedron

8 Node hexahedral element is used for 3D stress and strain analysis.
It is defined by eight nodes having three degrees of freedom at each node: translations in the nodal x, y, and z directions
It is trilinear because of the linear terms in x , y and z for the x , y and z displacement functions.
Standard element is based on pure displacement formulation which leads to shear and volumetric locking.
SCIFESOL provides Enhanced assumed strain (EAS) and B-Bar formulation to remove shear and volumetric locking in the element.