A finite-element formulation for geometrically exact multi-layer beams is proposed in the present work. The interlayer slip and uplift are not considered. The number of layers is arbitrary, and the basic unknown functions are the horizontal and vertical displacements of the composite beam’s reference axis and the cross-sectional rotation of each layer. Due to the geometrically exact definition of the problem, the governing equations are nonlinear in terms of basic unknown functions and the solution is obtained numerically. In general, each layer can have different geometrical and material properties, but since the layers are rigidly connected, the main application of this model is on homogeneous layered beams. Numerical examples compare the results of the present model with the existing geometrically nonlinear sandwich beam models and also with the 2D plane-stress elements and, where applicable, with the results from the theory of elasticity. The comparison with 2D plane-stress elements shows that the multi-layer beam model is very efficient for modelling thick beams where warping of the cross-section has to be considered.
Beam Theory Composite Beam Sandwich Beam Multilayer Beam Material Coordinate System
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.
Girhammar U.A., Pan D.H.: Exact static analysis of partially composite beams and beam-columns. Int. J. Mech. Sci. 49, 239–255 (2007)CrossRefGoogle Scholar
Irschik H., Gerstmayr J.: A continuum mechanics based derivation of reissner’s large-displacement finite-strain beam theory: the case of plane deformations of originally straight Bernoulli-Euler beams. Acta Mech. 206(1–2), 1–21 (2009)CrossRefzbMATHGoogle Scholar
Jelenić, G.: Finite element discretisation of 3D solids and 3D beams obtained by constraining the continuum. Technical report, Imperial College London, Department of Aeronautics, Aero Report 2004-01 (2004)Google Scholar
Kroflič A., Planinc I., Saje M., Čas B.: Analytical solution of two-layer beam including interlayer slip and uplift. Struct. Eng. Mech. 34(6), 667–683 (2010)CrossRefGoogle Scholar
Kroflič A., Saje M., Planinc I.: Non-linear analysis of two-layer beams with interlayer slip and uplift. Comput. Struct. 89(23–24), 2414–2424 (2011)Google Scholar
Ogden R.W.: Non-linear Elastic Deformations. Dover, New York (1997)Google Scholar
Reissner E.: On one-dimensional finite-strain beam theory; the plane problem. J. Appl. Math. Phys. (ZAMP) 23(5), 795–804 (1972)CrossRefzbMATHGoogle Scholar
Schnabl S., Planinc I., Saje M., Čas B., Turk G.: An analytical model of layered continuous beams with partial interaction. Struct. Eng. Mech. 22(3), 263–278 (2006)CrossRefGoogle Scholar
Schnabl S., Saje M., Turk G., Planinc I.: Analytical solution of two-layer beam taking into account interlayer slip and shear deformation. J. Struct. Eng. ASCE 133(6), 886–894 (2007)CrossRefGoogle Scholar
Simo J.C., Taylor R.L.: Quasi-incompressible finite elasticity in principal stretches: continuum basis and numerical algorithms. Comput. Methods Appl. Mech. Eng. 85, 273–310 (1991)CrossRefzbMATHMathSciNetGoogle Scholar
Simo J.C., Vu-Quoc L.: On the dynamics of flexible beams under large overall motions—the plane case: part i and ii. J. Appl. Mech. 53(4), 849–863 (1986)CrossRefzbMATHGoogle Scholar
Simo J.C., Vu-Quoc L.: A geometrically exact rod model incorporating shear and torsion-warping deformation. Int. J. Solids Struct. 27(3), 371–393 (1991)CrossRefzbMATHMathSciNetGoogle Scholar
Sousa J.B.M. Jr., da~Silva A.R.: Analytical and numerical analysis of multilayered beams with interlayer slip. Eng. Struct. 32, 1671–1680 (2010)CrossRefGoogle Scholar
Škec L., Schnabl S., Planinc I., Jelenić G.: Analytical modelling of multilayer beams with compliant interfaces. Struct. Eng. Mech. 44(4), 465–485 (2012)CrossRefGoogle Scholar
Timoshenko S.P., Goodier J.N.: Theory of Elasticity. McGraw-Hill, New York (1951)zbMATHGoogle Scholar
Vu-Quoc L., Deng H.: Galerkin projection for geometrically exact sandwich beams allowing for ply drop-off. J. Appl. Mech. 62, 479–488 (1995)CrossRefzbMATHGoogle Scholar
Vu-Quoc L., Ebcioğlu I.K.: General multilayer geometrically-exact beams and 1-d plates with piecewise linear section deformation. J. Appl. Math. Mech. (ZAMM) 76(7), 391–409 (1996)CrossRefzbMATHGoogle Scholar
Zienkiewicz O.C., Taylor R.L.: The Finite Element Method for Solid and Structural Mechanics. Butterworth-Heinemann, Oxford UK (2005)zbMATHGoogle Scholar
Zienkiewicz O.C., Taylor R.L., Zhu J.Z.: The Finite Element Method. Its Basis & Fundamentals. Butterworth-Heinemann, Oxford (2005)Google Scholar