What is the stiffness matrix method?
The Stiffness method provides a very systematic way of analyzing determinate and indeterminate structures. Displacement (Stiffness) Method. Express local (member) force-displacement. relationships in terms of unknown member. displacements.
What is stiffness matrix in structural analysis?
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.
What happens if determinant of stiffness matrix is zero?
From linear algebra we know that if an eigenvalue of a matrix becomes zero, it’s determinant also becomes zero and hence matrix becomes singular or non-invertible.
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.
How do you find the stiffness of a 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.
Why is a 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.
What is singular stiffness matrix?
A singular matrix merely means that you have not supplied sufficient information to uniquely solve the problem. This usually will require that the free modes of the system be restrained. For example, you might fix one point in space to prevent translation.
What is a global stiffness matrix?
The global stiffness matrix, [K]*, of the entire structure is obtained by assembling the element stiffness matrix, [K]i, for all structural members, ie. ( M-members) and expressed as. (1) where [K]i, is the stiffness matrix of a typical truss element, i, in terms of global axes.
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.
What is stiffness physics?
Stiffness is the extent to which an object resists deformation in response to an applied force.
What is flexibility matrix?
Flexibility matrix refers to the adaptability strategy, additionally called the technique for reliable deformations. In this matrix, there are basic unknown member forces. This method is widely used in analyzing beams, frames, and trusses.
Why stiffness matrix is symmetric?
The stiffness matrix is symmetric because for many material models and modeling assumptions, this is consistent with the physics happening at the level that we are studying. But oftentimes the stiffness matrix is NOT symmetric. There are a number of modeling scenarios for which this symmetry doesn’t hold.
What is a singular stiffness matrix?
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. So unless you add that information into the problem, the matrix will be singular.
What is an element stiffness matrix?
The element stiffness matrix is zero for most values of i and j, for which the corresponding basis functions are zero within Tk. The full stiffness matrix A is the sum of the element stiffness matrices. In particular, for basis functions that are only supported locally, the stiffness matrix is sparse .
