TY - JOUR

T1 - Viscoelastic Timoshenko beam theory

AU - Hilton, Harry H.

N1 - Funding Information:
Acknowledgement Support by grants from the Technology Research, Education an Commercialization Center (TRECC) of the National Center for Supercomputing Applications (NCSA) at the University of Illinois at Urbana-Champaign (UIUC) is gratefully acknowledged.

PY - 2009

Y1 - 2009

N2 - The concept of elastic Timoshenko shear coefficients is used as a guide for linear viscoelastic Euler-Bernoulli beams subjected to simultaneous bending and twisting. It is shown that the corresponding Timoshenko viscoelastic functions now depend not only on material properties and geometry as they do in elasticity, but also additionally on stresses and their time histories. Possible viscoelastic definitions are formulated and evaluated. In general, the viscoelastic relations are sufficiently complicated so that the elastic-viscoelastic correspondence principle (analogy) cannot be applied. This is particularly true for, but not limited to, elastic shear coefficients which are Poisson ratio dependent. Expressions for equivalent viscoelastic Timoshenko shear functions must, therefore, be derived de novo on a case by case basis, taking in to account specific relaxation moduli, stresses, temperatures and their time histories. Thus the elastic simplicity and generality is lost and hence rendering the use of viscoelastic Timoshenko shear functions as highly impractical. Consequently, it is necessary to directly solve the coupled viscoelastic beam governing relations for bending and twisting deflections by using appropriate solution protocols as discussed herein.

AB - The concept of elastic Timoshenko shear coefficients is used as a guide for linear viscoelastic Euler-Bernoulli beams subjected to simultaneous bending and twisting. It is shown that the corresponding Timoshenko viscoelastic functions now depend not only on material properties and geometry as they do in elasticity, but also additionally on stresses and their time histories. Possible viscoelastic definitions are formulated and evaluated. In general, the viscoelastic relations are sufficiently complicated so that the elastic-viscoelastic correspondence principle (analogy) cannot be applied. This is particularly true for, but not limited to, elastic shear coefficients which are Poisson ratio dependent. Expressions for equivalent viscoelastic Timoshenko shear functions must, therefore, be derived de novo on a case by case basis, taking in to account specific relaxation moduli, stresses, temperatures and their time histories. Thus the elastic simplicity and generality is lost and hence rendering the use of viscoelastic Timoshenko shear functions as highly impractical. Consequently, it is necessary to directly solve the coupled viscoelastic beam governing relations for bending and twisting deflections by using appropriate solution protocols as discussed herein.

KW - Timoshenko beams

KW - Timoshenko shear coefficients and functions

KW - Viscoelasticity

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U2 - 10.1007/s11043-008-9075-4

DO - 10.1007/s11043-008-9075-4

M3 - Article

AN - SCOPUS:60749131299

VL - 13

SP - 1

EP - 10

JO - Mechanics of Time-Dependent Materials

JF - Mechanics of Time-Dependent Materials

SN - 1385-2000

IS - 1

ER -