Table of Contents
What is the significance of serendipity elements?
The main advantage of the serendipity elements is that since the internal nodes of the higher-order Lagrange elements do not contribute to the inter-element connectivity, the elimination of internal nodes results in reductions in the size of the element matrices.
What is a serendipity element?
Serendipity Elements :- Serendipity elements are the rectangular elements which have no interior nodes. i.e all nodes lie on the boundary of the elements.
How do serendipity elements differ from Lagrangian elements?
The Lagrangian elements have interior nodes, while the serendipity elements only have exterior nodes. It can be seen that for higher order elements, the number of interior nodes quickly increases with order of the element.
What are Lagrangian and serendipity elements in FEM?
Lagrangian element can replicate any quadratic function. But Serendipity element can replicate most quadratic functions but not all. That is, Lagrangian elements are complete upto the quadratic order whereas Serendipity elements are complete only up to the linear order.
What are Lagrangian and serendipity elements?
What are the properties of shape functions?
Characteristic of Shape function
- Value of shape function of particular node is one and is zero to all other nodes.
- Sum of all shape function is one.
- Sum of the derivative of all the shape functions for a particular primary variable is zero.
What are axisymmetric elements?
Axisymmetric elements are triangular tori such that each element is symmetric with respect to geometry and loading about an axis such as the z axis. Hence, the z axis is called the axis of symmetry or the axis of revolution. Each vertical cross section of the element is a plane triangle.
What is meant by CST element?
In numerical mathematics, the constant strain triangle element, also known as the CST element or T3 element, is a type of element used in finite element analysis which is used to provide an approximate solution in a 2D domain to the exact solution of a given differential equation.
What is static condensation in FEM?
Static condensation is a process of eliminating or condensing some unknown DOF (known as secondary or slave DOF) and re-cast the original Eq. set (9.1) in terms of fewer unknowns (termed as primary unknowns or master DOF).