Quasi-static and dynamical analysis for viscoelastic Timoshenko beam with fractional derivative constitutive relation

Zhu, Zhihui; Gen-guo, LI; Chang-jun, Cheng

doi:10.1007/bf02437724

Cited by 47 publications

(12 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In his analysis, Chen assumed that the Poisson ratio is constant. This assumption is consistent with the findings of Zheng-you et al [15], who presented analytical solutions for Timoshenko beams with time-dependent and time-independent Poisson's ratios. Aköz and Kadioglu [13] presented two Timoshenko beam finite elements using the Laplace-Carson method and a mixed formulation.…”

Section: Introductionsupporting

confidence: 82%

Nonlinear quasi‐static finite element formulations for viscoelastic Euler–Bernoulli and Timoshenko beams

Payette

Reddy

2009

Numer Methods Biomed Eng

View full text Add to dashboard Cite

SUMMARYWeak form finite element models for the nonlinear quasi-static bending and extension of initially straight viscoelastic Euler-Bernoulli and Timoshenko beams are developed using the principle of virtual work. The mechanical properties of the beams are considered to be linear viscoelastic. However, large transverse displacements, moderate rotations and small strains are allowed by retaining the von Kármán strain components of the Green-Lagrange strain tensor in the formulation. The fully discretized finite element equations are developed using the trapezoidal rule in conjunction with a two-point recurrence relation. The resulting finite element equations, therefore, necessitate data storage from the previous time step only, and not the entire deformation history. Membrane locking is eliminated from the Euler-Bernoulli formulation through the use of selective reduced Gauss-Legendre quadrature. Membrane and shear locking are both circumvented in the Timoshenko beam finite element by employing a family of high-order Lagrange polynomials. A Newton-Raphson iterative scheme is used to solve the nonlinear finite element equations.

show abstract

Section: Introductionsupporting

confidence: 82%

Nonlinear quasi‐static finite element formulations for viscoelastic Euler–Bernoulli and Timoshenko beams

Payette

Reddy

2009

Numer Methods Biomed Eng

View full text Add to dashboard Cite

show abstract

“…We note in passing that effective temporal integration algorithms for alternative classes of viscoelastic constitutive equations, such as fractional derivative models, have also been adopted in the literature (see for example Refs. [10,11,12,15,42]…”

Section: Kinematics Of Deformationmentioning

confidence: 99%

A Nonlinear Finite Element Framework for Viscoelastic Beams Based on the High-Order Reddy Beam Theory

Payette¹,

Reddy

2013

Journal of Engineering Materials and Technology

View full text Add to dashboard Cite

A weak form Galerkin finite element model for the nonlinear quasi-static and fully transient analysis of initially straight viscoelastic beams is developed using the kinematic assumptions of the third-order Reddy beam theory. The formulation assumes linear viscoelastic material properties and is applicable to problems involving small strains and moderate rotations. The viscoelastic constitutive equations are efficiently discretized using the trapezoidal rule in conjunction with a two-point recurrence formula. Locking is avoided through the use of standard low-order reduced integration elements as well through the employment of a family of elements constructed using high-polynomial order Lagrange and Hermite interpolation functions.

show abstract

“…Akoz and Kadioglu [2] applied the correspondence principle and a numerical inverse transform method to discuss the quasi-static and dynamical behavior of a viscoelastic Timoshenko beam. Zhu et al [4] analyzed the quasi-static behavior of the viscoelastic Timoshenko beam under the step loading by using a three-dimensional fractional derivative constitutive relation. The analytical solution is obtained and the influence of material parameters on the deflection is investigated.…”

Section: Introductionmentioning

confidence: 99%

Quasi-static analysis for viscoelastic Timoshenko beams with damage

2006

View full text Add to dashboard Cite

Based on convolution-type constitutive equations for linear viscoelastic materials with damage and the hypotheses of Timoshenko beams, the equations governing quasi-static and dynamical behavior of Timoshenko beams with damage were first derived. The quasi-static behavior of the viscoelastic Timoshenko beam under step loading was analyzed and the analytical solution was obtained in the Laplace transformation domain. The deflection and damage curves at different time were obtained by using the numerical inverse transform and the influences of material parameters on the quasi-static behavior of the beam were investigated in detail.

show abstract

Quasi-static and dynamical analysis for viscoelastic Timoshenko beam with fractional derivative constitutive relation

Cited by 47 publications

References 6 publications

Nonlinear quasi‐static finite element formulations for viscoelastic Euler–Bernoulli and Timoshenko beams

Nonlinear quasi‐static finite element formulations for viscoelastic Euler–Bernoulli and Timoshenko beams

A Nonlinear Finite Element Framework for Viscoelastic Beams Based on the High-Order Reddy Beam Theory

Quasi-static analysis for viscoelastic Timoshenko beams with damage

Contact Info

Product

Resources

About