Equilibrium Equation Solvers
Linear Structural Analysis Solvers
In static analysis , simultaneous equations of the system are represented in matrix format as
SCIFESOL uses multifrontal solver UMFPACK to solve static equilibrium equations . UMFPACK is a set of routines for solving unsymmetric sparse linear systems, Ax=b, using the unsymmetric multifrontal method.
In dynamic analysis of structures , simultaneous equations of the system arise which are represented in matrix format as
which is known as dynamic equilibrium equation.
[m] = mass matrix , [c] = damping matrix , [k] = stiffness matrix , [ F] = load vector .
SCIFESOL uses two methods to solve dynamic equilibrium equations
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Direct integration methods like Newmark and Wilson - theta implicit time integration schemes.
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Mode Superposition method which uses natural frequencies and mode shapes from the modal analysis to characterize the transient dynamic response of a structure.
Modal Analysis Solver
Modal analysis is the process of determining dynamic characteristics of a system in forms of
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Natural frequencies
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Mode shapes
Modal analysis is used to form the modal model which is used for dynamic structural analysis.
SCIFESOL uses three methods to calculate Natural frequency and mode shapes of the structure
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Inverse Vector Iteration Method.
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Subspace Iteration Method.
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Jacobi Method.