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A mixed mass matrix for initial conditions is derived.
It has found that all three methods of lumpinglead to the same mass matrix for nine-node rectangular elements.
The method uses experimentally identified complex modes and complex natural frequencies, together with the knowledge of the mass matrix for the system.
The mass matrix for Gauss Lobatto grid points is usually approximated by Gauss Lobatto quadrature because this leads to a diagonal matrix that is easy to invert.
On the right-hand side of (14), the first matrix is the consistent mass matrix for intermediate and sink vertices; and, the second matrix is the discrete transport operator for source vertices only, i.e., the required form.
Notably, conservation is achieved with lumped mass, as opposed to the more commonly used Fluid Implicit Particle (FLIP) [2], [3] transfers which require a "full" mass matrix for exact conservation.
Similar(50)
Elastic stiffness and mass matrices for the non-symmetric cross-sections are precisely evaluated.
The closed-form solutions of the element stiffness and mass matrices for the flexure hinge are obtained.
The analytical free vibration analysis results were used to confirm the reliability of the presented stiffness and mass matrices for the arch element.
The application of layerwise theories to correctly model the displacement field of sandwich structures or laminates with high modulus ratios usually employs plate or facet-shell finite element formulations to compute the element stiffness and mass matrices for each layer.
Within the proposed computational scheme, both Euler-Bernoulli and Timoshenko beam theories have been adopted such that the explicit stiffness and mass matrices for 2-D FGP beam element through both beam theories are explicitly expressed.
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