On the analytical closed-form solution of high-order kinematic models in laminated beam theory. (English) Zbl 0981.74032

Summary: Analytical closed-form solutions of arbitrary composite laminates are derived for different high-order kinematic models violating the Euler-Bernoulli classical beam assumptions. The solutions are obtained with the aid of mathematical symbolic compiler MAPLE and are applied to exact stiffness matrices and to exact equivalent end actions. A study of feasibility of the procedure, in terms of accuracy requirements and computation volume, is also carried out.


74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74E30 Composite and mixture properties
68W30 Symbolic computation and algebraic computation
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics


Full Text: DOI


[1] Timoshenko, Philosophical Magazine, Series 6 41 pp 744– (1921)
[2] Vibration Problems in Engineering (2nd edn). Van Nostrand, Amsterdam, 1937; 337-338.
[3] Mindlin, ASME, Journal of Applied Mechanics 73 pp 31– (1951)
[4] Rakesh, AIAA Journal 27 pp 923– (1989)
[5] Effect of transverse shearing on cylindrical bending, vibration and buckling of laminated plates. AIAA, Paper No. 85-0744 cp., 1985.
[6] Bickford, Developments in Theoretical and Applied Mechanics 11 pp 137– (1982)
[7] Sheinman, International Journal for Numerical Methods in Engineering 39 pp 2155– (1996)
[8] Maple V Release 5.1. Waterloo Maple Inc., 1998.
[9] Nelson, ASME, Journal of Applied Mechanics 96 pp 177– (1974)
[10] Reissner, International Journal of Solids and Structures 11 pp 569– (1975)
[11] Lo, ASME, Journal of Applied Mechanics 99 pp 663– (1977) · Zbl 0369.73052
[12] Whitney, ASME, Journal of Applied Mechanics 44 pp 471– (1974) · Zbl 0295.73070
[13] Sheinman, ASME, Journal of Applied Mechanics 54 pp 558– (1987)
[14] Reddy, ASME, Journal of Applied Mechanics 51 pp 745– (1984)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.