Solving non-linear viscoelastic problems via a self-adaptive precise algorithm in time domain

Yang, Haitian; Han, Zhi

doi:10.1016/j.ijsolstr.2004.04.033

Cited by 14 publications

(6 citation statements)

References 19 publications

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“…On the other side, a differential‐integral equation system with boundary and initial values is converted into a series of recursive boundary value problems that can be solved by well‐developed numerical techniques such as FEM. By virtue of the proposed algorithm, the instantaneous elastic and long‐time critical loads can be determined in the static viscoelastic stability analysis, and the critical time can be evaluated in dynamic viscoelastic stability analysis. And, the static critical loads at short and long terms can be obtained directly by blocking the dashpot or vanishing rates. Numerical verification indicates that the proposed approach is capable of solving viscoelastic stability problems and can be expected as an efficient tool dealing with the problem that is difficult to be solved by analytical approach because of the more complex viscoelastic constitutive models and more complex boundary/initial conditions. As a by‐product, two analytical expressions are derived for the dynamic stability analysis of linear and Burgers models, respectively.Frankly, the work presented in this paper is a try of the expression technique in the linear viscoelastic stability analysis; actually, the proposed expression technique was employed for the nonlinear dynamic analysis, nonlinear viscoelastic analysis, and transient analysis of nonlinear heat transfer problems (Please see , Yang and Gao 2003); we do hope to extend our present and previous works to the nonlinear viscoelastic stability analysis, and make new contribution.…”

Section: Resultsmentioning

confidence: 92%

Numerical analysis of static and dynamic stabilities of viscoelastic columns

Yang

Han

2016

Math Methods in App Sciences

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This paper presents a new numerical approach for the static and dynamic stabilities analysis of viscoelastic columns. By expanding all variables in a discretized time interval, a time and space coupled integral-differential equation system is converted into a series of recursive spatial problems that are solved via FEM. A temporally piecewised adaptive algorithm is developed to maintain computing accuracy. Consequently, the descriptions of static stability of imperfect viscoelastic columns and dynamic stability of perfect viscoelastic columns are realized, respectively. Numerical examples are presented to verify the proposed approach. Additionally, two analytical expressions are derived for the dynamic stability analysis of linear and Burgers models, respectively.

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Section: Resultsmentioning

confidence: 92%

Numerical analysis of static and dynamic stabilities of viscoelastic columns

Yang

Han

2016

Math Methods in App Sciences

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“…Finally, according to Eqs. (4) and (5), the results at time t lþ1 can be obtained as follows: Table 1 Distributions of the known and unknown quantities in Eq. (39).…”

Section: Self-adaptive Checkmentioning

confidence: 99%

“…Up to now, the method combining the precise time-domain algorithm with FEM or Meshless method has been applied to many fields, such as heat transfer problems [4] and viscoelastic problems [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Precise time-domain expanding dual reciprocity boundary element method for solving transient heat conduction problems

Zhou

Chen

et al. 2015

International Journal of Heat and Mass Transfer

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“…(20) can be obtained. At the first time interval, t ∈ [τ 0 , τ 0 + T 1 ], using the precise algorithm, one has [17] …”

Section: Recurrent Constitutive Equationsmentioning

confidence: 99%

Solving viscoelastic problems with cyclic symmetry via a precise algorithm and EFGM

2006

Self Cite

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The paper combines a self-adaptive precise algorithm in the time domain with Meshless Element Free Galerkin Method (EFGM) for solving viscoelastic problems with rotationally periodic symmetry. By expanding variables at a discretized time interval, the variations of variables can be described more precisely, and iteration is not required for non-linear cases. A space-time domain coupled problem with initial and boundary values can be converted into a series of linear recursive boundary value problems, which are solved by a group theory based on EFGM. It has been proved that the coefficient matrix of the global EFG equation for a rotationally periodic system is block-circulant so long as a kind of symmetry-adapted reference coordinate system is adopted, and then a partitioning algorithm for facilitating parallel processing was proposed via a completely orthogonal group transformation. Therefore instead of solving the original system, only a series of independent small sub-problems need to be solved, leading to computational convenience and a higher computing efficiency. Numerical examples are given to illustrate the full advantages of the proposed algorithm.

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Solving non-linear viscoelastic problems via a self-adaptive precise algorithm in time domain

Cited by 14 publications

References 19 publications

Numerical analysis of static and dynamic stabilities of viscoelastic columns

Numerical analysis of static and dynamic stabilities of viscoelastic columns

Precise time-domain expanding dual reciprocity boundary element method for solving transient heat conduction problems

Solving viscoelastic problems with cyclic symmetry via a precise algorithm and EFGM

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