What is lumped mass matrix in FEM?
We have considered mass of the element as uniformly distributed throughout the element. Hence, these mass matrices are called as consistent matrices. We distribute the complete mass of the element at the two nodes. The mass matrix formed in this way is called as lumped mass matrix.
What are two types of mass matrix?
The construction of the mass matrix of individual elements can be carried out through several methods. These can be categorized into three groups: direct mass lumping, variational mass lumping, and template mass lumping. The last group is more general in that includes all others.
When the complete mass of the element is distributed equally at the two nodes of a element then mass matrices What are they known as?
Mass matrix computed by considering mass to be distributed equally at the two nodes of the element is known as lumped mass matrix.
What is a consistent matrix?
A linear system is consistent if and only if its coefficient matrix has the same rank as does its augmented matrix (the coefficient matrix with an extra column added, that column being the column vector of constants).
What is lumped mass idealization?
Lumped mass idealization is used to discretize the original beam structure with distributed mass to a weightless beam with distributed masses substituted with lumped masses at different nodal points. A numerical example obtained from literature is given to illustrate the application of the present model.
What is a lumped system?
A lumped system is one in which the dependent variables of interest are a function of time alone. In general, this will mean solving a set of ordinary differential equations (ODEs) A distributed system is one in which all dependent variables are functions of time and one or more spatial variables.
What makes a matrix inconsistent?
A system of linear equations can have no solution, a unique solution or infinitely many solutions. The rref of the matrix for an inconsistent system has a row with a nonzero number in the last column and 0’s in all other columns, for example 0 0 0 0 1.
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