Saddle-point principles and numerical integration methods for second-order hyperbolic equations

DOI10.1016/S0045-7825(00)00195-XzbMath1005.74076OpenAlexW1965097738MaRDI QIDQ1841039

Angelo Carini, Francesco Genna

Publication date: 19 February 2003

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0045-7825(00)00195-x

zbMATH Keywords

variational formulationstime integrationstructural dynamicssaddle-point principlescontinuous/discontinuous Galerkin formulationweak Hamilton/Ritz formulation

Mathematics Subject Classification ID

Numerical approximation of solutions of dynamical problems in solid mechanics (74H15)

Related Items (2)

Analytical integrations for the approximation of 3D hyperbolic scalar boundary integral equations ⋮ On the construction of extended problems and related functionals for general nonlinear equations

Cites Work

• Unnamed Item
• Unnamed Item
• Variational formulation for every nonlinear problem
• The Galerkin formulation and the Hamilton-Ritz formulation: A critical review
• Dynamics and the calculus of variations
• The method of Ritz applied to the equation of Hamilton
• Extremum principles for linear initial-value problems of mathematical physics
• A comprehensive unified set of single-step algorithms with controllable dissipation for dynamics. I: Formulation. II: Algorithms and analysis
• Computational algorithms for transient analysis: The burden of weight and consequences towards formalizing discrete numerically assigned [DNA algorithmic markers: \(W_p\)-family]
• Some variational formulations for continuum nonlinear dynamics
• Formulation and analysis of variational methods for time integration of linear elastodynamics
• Weighting functions in single-step algorithms for a non-linear equation
• A unified set of single step algorithms. Part 1: General formulation and applications
• Complementary variational principles in elastodynamics
• Dynamic response of mechanical systems by a weak Hamiltonian formulation
• Variational principles for operator equations and initial value problems
• Finite Elements for Initial Value Problems in Dynamics
• The temporal finite element method in structural dynamics
• Time finite element methods for structural dynamics
• Weighting parameters for unconditionally stable higher-order accurate time step integration algorithms. Part 2?second-order equations
• Computational schemes for non-linear elasto-dynamics
• UNCONDITIONALLY STABLE HIGHER-ORDER ACCURATE HERMITIAN TIME FINITE ELEMENTS
• A Comprehensive Energy Formulation for General Nonlinear Material Continua
• Saddle-Point Principles for General Nonlinear Material Continua
• An energetic formulation for the linear viscoelastic problem. Part I: Theoretical results and first calculations
• Variational principles for linear initial-value problems
• Transient field problems: Two‐dimensional and three‐dimensional analysis by isoparametric finite elements
• On the construction of extended problems and related functionals for general nonlinear equations

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