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Effective computation of restoring force vector in finite element method

Martin Balazovjech, Ladislav Halada (2007)

Kybernetika

We introduce a new way of computation of time dependent partial differential equations using hybrid method FEM in space and FDM in time domain and explicit computational scheme. The key idea is quick transformation of standard basis functions into new simple basis functions. This new way is used for better computational efficiency. We explain this way of computation on an example of elastodynamic equation using quadrilateral elements. However, the method can be used for more types of elements and...

Efficient application of e-invariants in finite element method for an elastodynamic equation

Martin Balazovjech, Ladislav Halada (2013)

Kybernetika

We introduce a new efficient way of computation of partial differential equations using a hybrid method composed from FEM in space and FDM in time domain. The overall computational scheme is explicit in time. The key idea of the suggested way is based on a transformation of standard basis functions into new basis functions. The results of this matrix transformation are e-invariants (effective invariants) with such suitable properties which save the number of arithmetical operations needed for a...

Energy methods for curved composite beams with partial shear interaction

István Ecsedi, Ákos József Lengyel (2015)

Curved and Layered Structures

This paper presents a derivation of the Rayleigh- Betti reciprocity relation for layered curved composite beams with interlayer slip. The principle of minimum of potential energy is also formulated for two-layer curved composite beams and its applications are illustrated by numerical examples. The solution of the presented problems are obtained by the Ritz method. The applications of the Rayleigh-Betti reciprocity relation proven are illustrated by some examples.

Error estimates for the ultra weak variational formulation in linear elasticity

Teemu Luostari, Tomi Huttunen, Peter Monk (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We prove error estimates for the ultra weak variational formulation (UWVF) in 3D linear elasticity. We show that the UWVF of Navier’s equation can be derived as an upwind discontinuous Galerkin method. Using this observation, error estimates are investigated applying techniques from the theory of discontinuous Galerkin methods. In particular, we derive a basic error estimate for the UWVF in a discontinuous Galerkin type norm and then an error estimate in the L2(Ω) norm in terms of the best approximation...

Error estimates for the ultra weak variational formulation in linear elasticity∗

Teemu Luostari, Tomi Huttunen, Peter Monk (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We prove error estimates for the ultra weak variational formulation (UWVF) in 3D linear elasticity. We show that the UWVF of Navier’s equation can be derived as an upwind discontinuous Galerkin method. Using this observation, error estimates are investigated applying techniques from the theory of discontinuous Galerkin methods. In particular, we derive a basic error estimate for the UWVF in a discontinuous Galerkin type norm and then an error estimate...

Error estimates of an iterative method for a quasistatic elastic-visco-plastic problem

Ioan Rosca, Mircea Sofonea (1994)

Applications of Mathematics

This paper deals with an initial and boundary value problem describing the quasistatic evolution of rate-type viscoplastic materials. Using a fixed point property, an iterative method in the study of this problem is proposed. A concrete algorithm as well as some numerical results in the one-dimensional case are also presented.

Error estimation and adaptivity for nonlinear FE analysis

Antonio Huerta, Antonio Rodríguez-Ferran, Pedro Díez (2002)

International Journal of Applied Mathematics and Computer Science

An adaptive strategy for nonlinear finite-element analysis, based on the combination of error estimation and h-remeshing, is presented. Its two main ingredients are a residual-type error estimator and an unstructured quadrilateral mesh generator. The error estimator is based on simple local computations over the elements and the so-called patches. In contrast to other residual estimators, no flux splitting is required. The adaptive strategy is illustrated by means of a complex nonlinear problem:...

Estensione di un teorema sull'adattamento in dinamica elasto-plastica

Claudia Comi, Alberto Corigliano (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Nell'articolo si tratta il problema dell'adattamento in dinamica elasto-plastica. La trattazione è fondata sulle seguenti basi: si adotta un legame costitutivo elasto-plastico di notevole generalità, basato su di una formulazione a variabili interne in grado di descrivere un comportamento incrudente genericamente non lineare; si fa riferimento ad un modello strutturale discreto, descritto mediante variabili generalizzate. I contributi presentati si possono così riassumere: si estendono risultati...

External approximation of first order variational problems via W-1,p estimates

Cesare Davini, Roberto Paroni (2008)

ESAIM: Control, Optimisation and Calculus of Variations

Here we present an approximation method for a rather broad class of first order variational problems in spaces of piece-wise constant functions over triangulations of the base domain. The convergence of the method is based on an inequality involving W - 1 , p norms obtained by Nečas and on the general framework of Γ-convergence theory.

Extremum theorem and convergence criterion for an iterative solution to the finite-step problem in elastoplasticity with mixed nonlinear hardening

Claudia Comi, Giulio Maier (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

For a class of elastic-plastic constitutive laws with nonlinear kinematic and isotropic hardening, the problem of determining the response to a finite load step is formulated according to an implicit backward difference scheme (stepwise holonomic formulation), with reference to discrete structural models. This problem is shown to be amenable to a nonlinear mathematical programming problem and a criterion is derived which guarantees monotonie convergence of an iterative algorithm for the solution...

Extremum theorems for finite-step back-ward-difference analysis of elastic-plastic nonlinearly hardening solids

Giulio Maier, Giorgio Novati (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

For the finite-step, backward-difference analysis of elastic-plastic solids in small strains, a kinematic (potential energy) and a static (complementary energy) extremum property of the step solution are given under the following hypotheses: each yield function is the sum of an equivalent stress and a yield limit; the former is a positively homogeneous function of order one of stresses, the latter a nonlinear function of nondecreasing internal variables; suitable conditions of "material stability"...

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