What is a global stiffness matrix?
For a more complex spring system, a ‘global’ stiffness matrix is required – i.e. one that describes the behaviour of the complete system, and not just the individual springs. From inspection, we can see that there are two springs (elements) and three degrees of freedom in this model, u1, u2 and u3.
How do you calculate 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.
What is global stiffness matrix in FEA?
[K] is the stiffness matrix of the entire structure – global stiffness matrix. {u} is the vector of displacements. The global stiffness matrix is constructed by assembling individual element stiffness matrices. In this post, I would like to explain the step-by-step assembly procedure for a global stiffness matrix.
Which conditions are applied to global stiffness matrix?
Condition of Compatibility – connected ends (nodes) of adjacent springs have the same displacements. Condition of Static Equilibrium – the resultant force at each node is zero. Constitutive Relation – that describes how the material (spring) responds to the applied loads.
What is the global stiffness method?
After developing the element stiffness matrix in the global coordinate system, they must be merged into a single “master” or “global” stiffness matrix. When merging these matrices together there are two rules that must be followed: compatibility of displacements and force equilibrium at each node.
Why is global stiffness matrix singular?
It mainly uses the member’s stiffness relations and displacements in structures. The global stiffness matrix is a singular matrix because its determinant is equal to zero.
What is global stiffness method called?
What is the Global stiffness method called? Explanation: Global stiffness matrix method makes use of the members stiffness relations for computing member forces and displacements in structures. Hence Global stiffness matrix or Direct stiffness matrix or Element stiffness matrix can be called as one. 11.
What is a lst element?
In this section we will develop a higher-order triangular element, called the linear-strain triangle (LST). This element has many advantages over the constant-strain triangle (CST). The LST element has six nodes and twelve displacement degrees of freedom. The displacement function for the triangle is quadratic.
What is local & global stiffness matrix?
The assembly of local stiffness matrices into a global stiffness matrix is carried out by enforcing continuity conditions along the interfaces which, in effect, leads to reformulation of the problem in terms of interfacial displacements as the basic unknown variables.
What is local and global stiffness matrix?
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.
Is global stiffness matrix singular?
Global stiffness matrix is a method of structural analysis that is used for computer automated analysis of complex structures. The global stiffness matrix is a singular matrix because its determinant is equal to zero.
How is the global stiffness matrix of a structure obtained?
Since we have already proven that K is symmetric, K is of a symmetric positive definite property. The global stiffness matrix, [K]*, of the entire structure is obtained by assembling the element stiffness matrix, [K] i, for all structural members, ie.
Which is an example of the stiffness method?
The Stiffness Method – Spring Example 1 Boundary conditions are of two general types: 1. homogeneous boundary conditions(the most common) occur at locations that are completely prevented from movement; 2. nonhomogeneous boundaryconditions occur where finite non-zero values of displacement are specified, such as the settlement of a support.
Why is the global stiffness matrix K J singular?
Note that the matrix is square and symmetric. Expansion of the determinant of this matrix would demonstrate that the matrix is singular [K J] = that the matrix is singular due to the fact that certain rows and columns are linear combinations of one another.
Is the element stiffness matrix invertible or symmetric?
The element stiffness matrix is “symmetric”, i.e. 2. The element stiffness matrix is singular, i.e., The consequence is that the matrix is NOT invertible. It is not possible to invert it to obtain the displacements.