Affiliation:
1. Computational Structures Branch, NASA Langley Research Center, MS 240, Hampton, VA 23681-0001
Abstract
A viscoelastic higher-order thick beam finite element formulation is extended to include elastodynamic deformations. The material constitutive law is a special differential form of the Maxwell solid, which employs viscous strains as internal variables to determine the viscous stresses. The total time-dependent stress is the superposition of its elastic and viscous components. In the constitutive model, the elastic strains and the conjugate viscous strains are coupled through a system of first-order ordinary differential equations. The use of the internal strain variables allows for a convenient finite element formulation. The elastodynamic equations of motion are derived from the virtual work principle. Computational examples are carried out for a thick orthotropic cantilevered beam. Relaxation, creep, relaxation followed by free damped vibrations, and damping related modal interactions are discussed.
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics,General Materials Science
Reference18 articles.
1. Halpin
J. C.
, and PaganoN. J., “Observations on Linear Anisotropic Viscoelasticity,” J. Composite Materials, Vol. 2, No. 1, pp. 68–80. 1968.
2. Hashin
Z.
, “Complex Moduli of Viscoelastic Composites—I. General Theory and Applications to Particulate Composites,” Int. J. Solids Structures, Vol. 6, pp. 539–552, 1970.
3. Hashin
Z.
, “Complex Moduli of Viscoelastic Composites—II. Fiber Reinforced Materials,” Int. J. Solids and Structures, Vol. 6, pp. 797–807, 1970.
4. Argyris
J.
, St. DoltsinisI., and daSilvaV. D., “Constitutive Modeling and Computation of Non-Linear Viscoelastic Solids, Part I. Rheological Models and Numerical Integration Techniques,” Comput. Methods Appl. Mech. Engrg., Vol. 88, pp. 135–163, 1991.
5. Shaw, S., Warby, M. K., and Whiteman, J. R., “Numerical Techniques for Problems of Quasistatic and Dynamic Viscoelasticity,” J. R. Whiteman, ed., The Mathematics of Finite Elements and Applications, Highlights 1993, pp. 45–68, Wiley, 1994.
Cited by
28 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献