A unified linear bending/shear beam (spar) theory: From deterministic da vinci-euler-bernoulli elastic beams to nonhomogeneous generalized linear viscoelastic Timoshenko ones with random properties, loads and realistic physical starting transients, and including moving shear centers and neutral axes, part I: Theoretical modeling and analyses

Harry H. Hilton

Research output: Contribution to journalArticlepeer-review


A unified bending/shear beam (spar) theory has been formulated by merging a number of previously completed theoretical segments into a comprehensive analytical treatment of linear non-homogenous viscoelastic Timoshenko beams (spars) with stochastic properties and random dynamic loads including shear center and neutral axis spatial and temporal motions due to bending, and including realistic physical starting load transients. These inverse problem analyses are framed entirely in terms of relaxation moduli or creep compliances, excluding any dependence on Poisson's ratios. The deterministic and stochastic effects of unequal tension and compression relaxation moduli/ compliances on normal and shear bending stresses are derived and evaluated. The influences of all these phenomena on combined bending and shear stress distributions, structural instabilities, material failures and structural survival times also are formulated and discussed.

Original languageEnglish (US)
Pages (from-to)277-314
Number of pages38
JournalMathematics in Engineering, Science and Aerospace
Issue number3
StatePublished - 2018


  • Da vinci-euler-bernoulli and timoshenko elastic and viscoelastic beams (spars)
  • Failures
  • Realistic starting transient loads
  • Shear center and neutral axis motions
  • Stochastic linear viscoelasticity
  • Survival times

ASJC Scopus subject areas

  • Modeling and Simulation
  • Aerospace Engineering
  • Applied Mathematics

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