The Tikhonov regularization method in elastoplasticity

Deus, Hilbeth P. Azikri de; Ávila, R S Claudio; Belo, Ivan Moura; Beck, André Teófilo

doi:10.1016/j.apm.2011.11.086

Cited by 3 publications

(5 citation statements)

References 29 publications

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“…where k β represents the thermodynamic forces associated to internal variables k α ( [6,1]) . The yield function.…”

Section: Materials Science Applied Mechanics and Advanced Engineering...mentioning

confidence: 99%

“…An important aspect of the yield function is the fact that it is subjected to the Kuhn-Tucker conditions ( [6]), i.e., ( )…”

Section: Materials Science Applied Mechanics and Advanced Engineering...mentioning

confidence: 99%

“…Many techniques for this objective can be found in specialized literature, commented in [5]. In this context, the L-curve technique has been widely applied in ill-posed problems, and was adopted in this work to determine the regularization parameter ( [5,6]).…”

Section: Incremental Formulationmentioning

confidence: 99%

“…This fourth order tensor operator is intimately related to the integral operator that generates, in a numerical point of view, the stiff matrices. One of the numerical aspects shown in [6] is the fact that points in the neighborhood of a critical point lead to ill-conditioned stiffness matrices, in a numerical sense.…”

Section: Introductionmentioning

confidence: 99%

“…the regularization parameter and the solution of (42) can be writen as (singular value decomposition) of A point of view, it can be proven the convergence of f to ([5,6])…”

mentioning

confidence: 99%

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Elastoplasticity 2D Problems: Numerical Applications of the Tikhonov Regularization Method

Silva

Deus

Silva

2015

AMM

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The numerical simulation is widely used, in now days, to verify the viability and to optimize structural mechanic designs. The numerical approach of elastoplastic materials can found some problems related to ill-conditioning of matrices (from FEM systems), associated to the critical points from the snap through or snap back shape of the equilibrium curve. Aiming to overcome this misfortune it is proposed a strategy via Tikhonov regularization method in association with L-curve technique to determine the regularization parameter. This strategy can be used in many numerical applications for structural analysis. The theoretical development about these Some numerical examples are presented to attest the efficiency of this proposed approach.

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“…where k β represents the thermodynamic forces associated to internal variables k α ( [6,1]) . The yield function.…”

Section: Materials Science Applied Mechanics and Advanced Engineering...mentioning

confidence: 99%

“…An important aspect of the yield function is the fact that it is subjected to the Kuhn-Tucker conditions ( [6]), i.e., ( )…”

Section: Materials Science Applied Mechanics and Advanced Engineering...mentioning

confidence: 99%

Section: Incremental Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…the regularization parameter and the solution of (42) can be writen as (singular value decomposition) of A point of view, it can be proven the convergence of f to ([5,6])…”

mentioning

confidence: 99%

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Elastoplasticity 2D Problems: Numerical Applications of the Tikhonov Regularization Method

Silva

Deus

Silva

2015

AMM

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An analysis on the shear modulus of the modified Jeffreys model

Deus

Silva

Itskov

2019

Applied Mathematics and Computation

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A novel method for force identification based on filter and FEM

Zheng

Wang

2019

Journal of Vibration and Control

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Force identification plays a vital role in vibration control and structural health monitoring. Force identification is an inverse problem to determine the excitation load from the responses. In general, the inverse problem has strong ill-posedness and ill-condition, especially in the case of low signal-to-noise ratio. Singular value decomposition and Tikhonov regularization are widely used for the reconstruction of the input force. Nevertheless, the anti-noise performance and accuracy of the two methods are still unsatisfactory. In this paper, we present a novel method for force identification based on a filter and the finite element method (FEM). The filter is used to suppress the noise of the input signals. FEM is introduced to reduce the discretization error and the regularization parameters are optimized by the genetic algorithm. After the signal is filtered, the characteristics of the signal will be changed. Especially, the initial and the last segments of the input signal will be lost. These changes may make the identified force inaccurate, even more inaccurate than the force identified with no filtering. To deal with this problem, cubic spline interpolation and a nonlinear autoregressive neural network are introduced to repair the input signals. Finally, three numerical examples and experiments are used to verify the superiority of the method.

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The Tikhonov regularization method in elastoplasticity

Cited by 3 publications

References 29 publications

Elastoplasticity 2D Problems: Numerical Applications of the Tikhonov Regularization Method

Elastoplasticity 2D Problems: Numerical Applications of the Tikhonov Regularization Method

An analysis on the shear modulus of the modified Jeffreys model

A novel method for force identification based on filter and FEM

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