Summary
A flexural theory of elastic sandwich beams is derived which renders quite precise results within a wide range of ratios of dimensions, mass densities, and elastic constants of the core and faces. The assumptions of the Timoshenko theory of shear-deformable beams are applied to each of the homogeneous, linear elastic, transversely isotropic layers individually. Core and faces are perfectly bonded. The principle of virtual work is applied to derive the equations of motion of a symmetrically designed three-layer beam and its boundary conditions. By definition of an effective cross-sectional rotation the complex problem is reduced to a problem of a homogeneous beam with effective stiffnesses and with corresponding boundary conditions. Thus, methods of classical mechanics become directly applicable to the higher-order problem. Excellent agreement of the results of illustrative examples is observed when compared to solutions of other higher-order laminate theories as well as to exact solutions of the theory of elasticity.
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Heuer, R. Static and dynamic analysis of transversely isotropic, moderately thick sandwich beams by analogy. Acta Mechanica 91, 1–9 (1992). https://doi.org/10.1007/BF01194029
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DOI: https://doi.org/10.1007/BF01194029