What is stiffness matrix 2d CST?
Write down the stiffness matrix equation for two dimensional CST elements. Stiffness matrix [K ]=[B ]T [D ][B ]At. [B]T -Strain displacement [D]-Stress strain matrix [B]-Strain displacement matrix. 2.
How do you find the stiffness of a matrix?
Let the force–displacement equation representing this system be { F } 6 × 1 = [ K ] 6 × 6 { d } 6 × 1 , where {d} represents three horizontal and three vertical displacements, {F} is the force vector, and [K] is the structure stiffness matrix.
What is structural stiffness matrix?
A stiffness matrix, [K], relates point forces, {p}, applied at a set of coordiantes on the structure , to the displacements, {d}, at the same set of coordinates. [K]{d} = {p} (1) The locations and directions of the point forces and displacements are called the coordinates of the structural model.
How do you calculate the size of the global stiffness matrix?
Since the spring element has two degrees of freedom, the interval elemental stiffness matrix is of order 2 × 2. Hence, for a system of n − 1 elements (n nodes), the size of the global stiffness matrix KG will be of order n × n.
How many DOF are there in CST?
Constant Strain Triangle (CST) with three degrees of freedom per node.
What is CST and LST in FEM?
CST – Constant Strain Triangle – First order Triangle Element – 3 nodes per Triangle. LST – Linear Strain Triangle – Second order Triangle Element – 6 nodes in Triangle.
Why is stiffness matrix singular?
A stiffness matrix that describes the deformation of an elastic body will in general be singular. Because any simple translation has no impact on the stored energy of deformation. As well, a simple rotation will also leave the energy unchanged.
Why is a stiffness matrix singular?
4.2. The stiffness matrix Ke in Eq. (4.28) is usually singular, because the whole structure can perform rigid body movements. There are two DOFs of rigid movements for planer trusses and three DOFs for space trusses. These rigid body movements are constrained by supports or displacement constraints.
What is the stiffness matrix for plane frame element?
Initially, the stiffness matrix of the plane frame member is derived in its local co-ordinate axes and then it is transformed to global co-ordinate system. This is achieved by transformation of forces and displacements to global co-ordinate system.