There are two possible geometric shapes: a triangle with the fourth node at the centroid of the triangle or a rectangle with nodes at the vertices.Ī triangle with a fourth node at the center does not provide a single-valued variation of u at inter-element boundaries, resulting in incompatible variation of u at inter-element boundaries and is therefore not admissible. The polynomial requires an element with four nodes. This polynomial contains four linearly independent terms and is linear in x and y, with a bilinear term in x and y. In order to find the three unknowns c 1 , c 2 and c 3 , we apply the boundary conditions Let us assume that the single variable can be expressed as If so, then the unknown single variable u (temperature) at any non-nodal point x, y in the 2-D domain can be expressed in terms of the known nodal variables (temperatures) u1, u 2 and u3. The single variable (for example, temperature) at these nodes 1, 2 and 3 are u1, u 2 and u3, respectively. Let us consider one such element with coordinates one such element with coordinates (x 1,y 1), (x 2,y 2), (x 3,y 3) . Each triangular element has three nodes, (i.e., one node at each corner). We consider such an area meshed with triangular elements. At each point there can be only one temperature. An example is the temperature distribution in a plate. (a scalar quantity, not a vector quantity).
The physical domain considered is geometrically a 2-Dimensional domain, i.e., an area with uniform thickness and the single variable can be one of pressure, temperature, etc. It is defined to be a state of strain in which the normal to the xy plane and the Stress ( t )directed perpendicular to the plane are assumed to be zero. It is defined to be a state of stress in which the normal stress ( s ) and shear The 2d element is extremely important for the Plane Stress analysis and Plane The basic element useful for two dimensional analysis is the Two dimensional elements are defined by three or more nodes in a two dimensional
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