The ultra weak variational formulation of thin clamped plate problems

DOI10.1016/j.jcp.2013.12.028zbMath1349.74330OpenAlexW2040185014MaRDI QIDQ348762

Teemu Luostari, Tomi Huttunen, Peter B. Monk

Publication date: 5 December 2016

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2013.12.028

zbMATH Keywords

fourth order problemclamped plateKirchhoff's thin platenon-polynomialultra weak variational formulationupwind discontinuous Galerkin method

Mathematics Subject Classification ID

Plates (74K20) Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

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Cites Work

• Unnamed Item
• An efficient wave based prediction technique for dynamic plate bending problems with corner stress singularities
• Solving Maxwell's equations using the ultra weak variational formulation
• An efficient wave based prediction technique for plate bending vibrations
• Linear integral equations.
• Computational aspects of the ultra-weak variational formulation
• Plane wave approximation of homogeneous Helmholtz solutions
• Discontinuous Galerkin methods with plane waves for time-harmonic problems
• The variational theory of complex rays for the calculation of medium‐frequency vibrations
• Plane wave approximation in linear elasticity
• Improvements for the ultra weak variational formulation
• Using Plane Waves as Base Functions for Solving Time Harmonic Equations with the Ultra Weak Variational Formulation
• A discontinuous enrichment method for the efficient solution of plate vibration problems in the medium-frequency regime
• Unique Continuation for Elliptic Equations
• Comparison of two wave element methods for the Helmholtz problem
• Application of an Ultra Weak Variational Formulation of Elliptic PDEs to the Two-Dimensional Helmholtz Problem
• The Ultra Weak Variational Formulation Using Bessel Basis Functions
• The Ultra-Weak Variational Formulation for Elastic Wave Problems
• The method of fundamental solutions applied to the calculation of eigensolutions for 2D plates
• The free vibration of rectangular plates
• The discontinuous enrichment method