A Mixed and Multi-Step Higher-Order Implicit Time Integration Family

Rezaiee‐Pajand, Mohammad; Sarafrazi, S. R.

doi:10.1243/09544062jmes2093

Cited by 34 publications

(44 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…4 of Ref. 28, it can be seen that the suggested algorithm has a smaller error than the Bathe, Wilson-and Newmark linear acceleration methods. The numerical solutions along with the exact ones of the problem in the small portion of time are shown in Fig.…”

Section: The Van Der Pol Equationmentioning

confidence: 81%

“…Following Ref. 28, the errors are also normalized with respect to the maximum value of x. Figure 7 shows the envelope curves of the positive normalized errors.…”

Section: The Van Der Pol Equationmentioning

confidence: 99%

“…Other researchers have analyzed this structure previously. 28,39 The lumped masses for the°oors are taken as m 1 ¼ m 2 ¼ m 3 ¼ m 4 ¼ m 5 ¼ 2:616 Ã 10 6 (kg). The sti®ness coe±cients are assumed to be k 1 ¼ 1177:2 Ã 10 6 (N/m) and k 2 ¼ k 3 ¼ k 4 ¼ k 5 ¼ 981 Ã 10 6 (N/m).…”

Section: A¯ve-story Shear Buildingmentioning

confidence: 99%

“…This problem was already solved by other investigators for comparing the accuracy of various time integration methods. 28,40 The following equation of motion for this system is held:…”

Section: A Two Dof Modelmentioning

confidence: 99%

“…19 Some of the conventional implicit methods are: Houbolt's method, 20 Newmark family, 9 Wilson-, 21 HHT-algorithm by Hilber et al, 22 WBZ-by Wood et al, 23 by Bazzi and Anderheggen, 24 and generalized-by Chung and Hulbert. 25 Several new implicit schemes have been presented including, Rezaiee-Pajand and Alamatian, 26,27 Rezaiee-Pajand and Sarafrazi, 28 Gholampour et al, 29 Ghassemieh and Karimi-Rad, 30 Gholampour and Ghassemieh 31 and Bathe and Baig. 32 Following the formulation similar to the Bathe method, a new explicit algorithm is suggested by Noh and Bathe.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A New Explicit Time Integration Scheme for Nonlinear Dynamic Analysis

Rezaiee‐Pajand

Karimi-Rad

2016

Int. J. Str. Stab. Dyn.

View full text Add to dashboard Cite

An explicit time integration method is presented for the linear and nonlinear dynamic analyses of structures. Using two parameters and employing the Taylor series expansion, a family of second-order accurate methods for the solution of dynamic problems is derived. The proposed scheme includes the central di®erence method as a special case, while damping is shown to exert no e®ect on the solution accuracy. The proposed method is featured by the following facts: (i) the relative period error is almost zero for speci¯c values of the parameters; (ii) the numerical dissipation contained can help¯lter out spurious high-frequency components; and (iii) the crucial lower modes are generally una®ected in the integration. Although the proposed method is conditionally stable, it has an appropriate region of stability, and is self-starting. The numerical tests indicate the improved performance of the proposed technique over the central di®erence method.

show abstract

Section: The Van Der Pol Equationmentioning

confidence: 81%

“…Following Ref. 28, the errors are also normalized with respect to the maximum value of x. Figure 7 shows the envelope curves of the positive normalized errors.…”

Section: The Van Der Pol Equationmentioning

confidence: 99%

Section: A¯ve-story Shear Buildingmentioning

confidence: 99%

“…This problem was already solved by other investigators for comparing the accuracy of various time integration methods. 28,40 The following equation of motion for this system is held:…”

Section: A Two Dof Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A New Explicit Time Integration Scheme for Nonlinear Dynamic Analysis

Rezaiee‐Pajand

Karimi-Rad

2016

Int. J. Str. Stab. Dyn.

View full text Add to dashboard Cite

show abstract

Improving stability domains of the implicit higher order accuracy method

Rezaiee‐Pajand

Sarafrazi

Hashemian

2011

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYThe implicit higher order accuracy (IHOA) time integration family has a high order of accuracy. However, its stability domains are very restrictive. By improving the stability conditions, the larger time steps can be utilized. In this study, two parameters are introduced in the displacement and velocity extrapolations of IHOA. In order to find the optimum values of the proposed parameters, the dissipation and the dispersion are investigated. Three conditionally stable versions of the second-, third-, and forth-order algorithms are found. It is shown that these formulations have larger stability domains than the previous ones. Furthermore, the suggested strategies give responses that are more accurate.

show abstract

Degenerated shell element with composite implicit time integration scheme for geometric nonlinear analysis

Zhang

Liu

2015

Numerical Meth Engineering

View full text Add to dashboard Cite

Summary A degenerated shell element with composite implicit time integration scheme is developed in the present paper to solve the geometric nonlinear large deformation and dynamics problems of shell structures. The degenerated shell element is established based on the eight‐node solid element, where the nodal forces, mass matrices, and stiffness matrices are firstly obtained upon virtual velocity principle and then translated to the shell element. The strain field is modified based on the mixed interpolation of tensorial components method to eliminate the shear locking, and the constitutive relation is modified to satisfy the shell assumptions. A simple and practical computational method for nonlinear dynamic response is developed by embedding the composite implicit time integration scheme into the degenerated shell element, where the composite scheme combines the trapezoidal rule with the three‐point backward Euler method. The developed approach can not only keep the momentum and energy conservation and decay the high frequency modes but also lead to a symmetrical stiffness matrix. Numerical results show that the developed degenerated shell element with the composite implicit time integration scheme is capable of solving the geometric nonlinear large deformation and dynamics problems of the shell structures with momentum and energy conservation and/or decay. Copyright © 2015 John Wiley & Sons, Ltd.

show abstract

A Mixed and Multi-Step Higher-Order Implicit Time Integration Family

Cited by 34 publications

References 40 publications

A New Explicit Time Integration Scheme for Nonlinear Dynamic Analysis

A New Explicit Time Integration Scheme for Nonlinear Dynamic Analysis

Improving stability domains of the implicit higher order accuracy method

Degenerated shell element with composite implicit time integration scheme for geometric nonlinear analysis

Contact Info

Product

Resources

About