Construction of Customized Mass-Stiffness Pairs Using Templates

Felippa, Carlos A.

doi:10.1061/(asce)0893-1321(2006)19:4(241)

Cited by 22 publications

(8 citation statements)

References 17 publications

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“…Here M Cij and χ Cij denote physical and dimensionless entries, respectively. The entry dependence on γ is omitted from (11) to reduce clutter. Their expressions may be found in Table 1.…”

Section: Fully Integrated Mass Matricesmentioning

confidence: 99%

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Mass-Stiffness Templates for Cubic Structural Elements

Felippa¹

2021

Computer Modeling in Engineering &Amp; Sciences

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Section: Fully Integrated Mass Matricesmentioning

confidence: 99%

“…A short history of templates, adapted from a recent survey paper [8] is given in Appendix A. The present paper is a specialized continuation of a 2015 survey paper [9] that studies massstiffness templates for structural dynamics in a more general context, following up on earlier work [10,11].…”

Section: Introductionmentioning

confidence: 99%

Mass-Stiffness Templates for Cubic Structural Elements

Felippa¹

2021

Computer Modeling in Engineering &Amp; Sciences

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“…This principle is a particular case of the general three-parametric template principle of elasto-dynamics with two free parameters set to minus one and zero, C 1 D 1 and C 3 D 0. For details of the penalized/template Hamiltonians and mass matrix templates, see [14,29] and [30,31], respectively. Variation of the latter principle leads to 440 A. TKACHUK AND M. BISCHOFF…”

Section: Derivation Of a One-parametric Family Of Inverse Consistent mentioning

confidence: 99%

“…A. TKACHUK AND M. BISCHOFF APPENDIX C: DISPERSION ANALYSIS OF 1D TWO-NODE ROD ELEMENT Dispersion relation for variationally scaled reciprocal mass matrices (VSRMM) is obtained with a method given in [30,53] for an infinite mesh of equal-sized elements (l e ) with uniform properties (A; E; ). The element matrices for two-node rod element read N D This yields the equations of motion for the n th node in the form P U n D 1 4Al e .. 2 C 3C 2 /P n 1 C .8 6C 2 /P n C .…”

mentioning

confidence: 99%

Direct and sparse construction of consistent inverse mass matrices: general variational formulation and application to selective mass scaling

Tkachuk

Bischoff

2014

Numerical Meth Engineering

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Classical explicit finite element formulations rely on lumped mass matrices. A diagonalized mass matrix enables a trivial computation of the acceleration vector from the force vector. Recently, non-diagonal mass matrices for explicit finite element analysis (FEA) have received attention due to the selective mass scaling (SMS) technique. SMS allows larger time step sizes without substantial loss of accuracy. However, an expensive solution for accelerations is required at each time step. In the present study, this problem is solved by directly constructing the inverse mass matrix. First, a consistent and sparse inverse mass matrix is built from the modified Hamiltons principle with independent displacement and momentum variables. Usage of biorthogonal bases for momentum allows elimination of momentum unknowns without matrix inversions and directly yields the inverse mass matrix denoted here as reciprocal mass matrix (RMM). Secondly, a variational mass scaling technique is applied to the RMM. It is based on the penalized Hamiltons principle with an additional velocity variable and a free parameter. Using element-wise bases for velocity and a local elimination yields variationally scaled RMM. Thirdly, examples illustrating the efficiency of the proposed method for simplex elements are presented and discussed.A. TKACHUK AND M. BISCHOFF Several algebraic methods for SMS are proposed in the literature. Mass penalty in thickness direction of solid-shell finite elements is proposed in [2,3]. This method adds artificial mass to the LMM for a relative motion in thickness direction for the nodes in the stacks of solid-shells. Such algebraic blocks reduce the highest thickness modes of the structure and at the same time are orthogonal to the bending modes, which allows accurate solutions for thin-walled structures. Stiffness proportional mass scaling ( ı D˛K) is described in [1,[4][5][6]. This method is accurate and allows preservation of the eigenvectors of the structure, but in case of non-linear problems, it requires reassembly of the scaled mass matrix for several times during the computation, because the stiffness matrix changes under large rotations and deformations [5]. The overhead introduced by reassembly is the main disadvantage of stiffness proportional mass scaling and the reason for not implementing the method in commertial finite element (FE) codes. This problem is partially resolved by the method described by Olovsson in [1]. This method uses an algebraically built template for added mass ı that does not change upon deformation and rotations. The kernel of this added mass ı includes the translational rigid body modes of individual elements, which mimics the stiffness proportional mass scaling. As a result of such a construction, the translational mass of individual elements is preserved. In addition, the method is easily implementable, and it is available in commercial codes, for example, LS-DYNA and RADIOSS. The implementation details are given in [7,8]. Further algebraic SMS methods scale the inertia of incom...

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“…Felippa proposed different methods to construct the mass matrix for beam elements [15]. He customized mass template for the two cases of vibration analysis and wave propagation.…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis of plane frames by customized stiffness and diagonal mass matrices

Rezaiee‐Pajand

Khajavi

2011

Proceedings of the Institution of Mechanical Engineers, Part C:

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This article presents a formulation for the vibration analysis of plane frames. The strain gradient notation is utilized to determine the mass and stiffness matrices. The obtained matrices can easily be parameterized due to their simple structure. Both Euler-Bernoulli- and Timoshenko-beam elements are investigated in this study. The parameterized stiffness and mass matrices are optimized for accurate performance in the vibration analysis of frame structures. Some numerical examples are solved to show the advantages of the presented scheme. Results of these sample vibration problems indicate that the proposed technique increases the accuracy of analysis, when these new stiffness and diagonal mass matrices are used.

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Construction of Customized Mass-Stiffness Pairs Using Templates

Cited by 22 publications

References 17 publications

Mass-Stiffness Templates for Cubic Structural Elements

Mass-Stiffness Templates for Cubic Structural Elements

Direct and sparse construction of consistent inverse mass matrices: general variational formulation and application to selective mass scaling

Vibration analysis of plane frames by customized stiffness and diagonal mass matrices

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