Inverse mass matrix for higher-order finite element method via localized Lagrange multipliers

Kód výsledku v IS VaVaI

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Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Inverse mass matrix for higher-order finite element method via localized Lagrange multipliers

Popis výsledku v původním jazyce

In this contribution, we pay an attention on an extension of the direct inversion of mass matrix for higher-order finite element method and its application for numerical modelling in structural dynamics. In works, the following formula for the inversion of the mass matrix M has been derived based on the Hamilton's principle as follows M-1 = A-TCA-1 where M is the mass matrix, M-1 is its inversion, C is labeled as the momentum matrix, A is the diagonal projection matrix. The final form of the inverse matrix mass is sparse, symmetrical and preserving the total mass. In the first step of the approach, the inverse mass matrix for the floating system is obtained and in the second step, the Dirichlet boundary conditions are applied via the method of Localized Lagrange Multipliers [3]. In the contribution, we discuss using different lumping approaches for the A-projection matrix based on Row-summing, Diagonal scaling method, Quadrature-based lumping and Manifold-based method. We analyze accuracy of obtained inverse mass matrices in free vibration problems and their convergence rates.

Název v anglickém jazyce

Inverse mass matrix for higher-order finite element method via localized Lagrange multipliers

Popis výsledku anglicky

In this contribution, we pay an attention on an extension of the direct inversion of mass matrix for higher-order finite element method and its application for numerical modelling in structural dynamics. In works, the following formula for the inversion of the mass matrix M has been derived based on the Hamilton's principle as follows M-1 = A-TCA-1 where M is the mass matrix, M-1 is its inversion, C is labeled as the momentum matrix, A is the diagonal projection matrix. The final form of the inverse matrix mass is sparse, symmetrical and preserving the total mass. In the first step of the approach, the inverse mass matrix for the floating system is obtained and in the second step, the Dirichlet boundary conditions are applied via the method of Localized Lagrange Multipliers [3]. In the contribution, we discuss using different lumping approaches for the A-projection matrix based on Row-summing, Diagonal scaling method, Quadrature-based lumping and Manifold-based method. We analyze accuracy of obtained inverse mass matrices in free vibration problems and their convergence rates.

Druh

O - Ostatní výsledky

CEP obor

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OECD FORD obor

20302 - Applied mechanics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů