A new refined theory for laminated composite and sandwich beams that contains the kinematics of the Timoshenko Beam Theory as a proper baseline subset is presented. This variationally consistent theory is derived from the virtual work principle and employs a novel piecewise linear zigzag function that provides a more realistic representation of the deformation states of transverse-shear flexible beams than other similar theories. This new zigzag function is unique in that it vanishes at the top and bottom bounding surfaces of a beam. The formulation does not enforce continuity of the transverse shear stress across the beam's cross-section, yet is robust. Two major shortcomings that are inherent in the previous zigzag theories, shear-force inconsistency and difficulties in simulating clamped boundary conditions, and that have greatly limited the utility of these previous theories are discussed in detail. An approach that has successfully resolved these shortcomings is presented herein. Exact solutions for simply supported and cantilevered beams subjected to static loads are derived and the improved modelling capability of the new "zigzag" beam theory is demonstrated. In https://ntrs.nasa.gov/search.jsp?R=20090020418 2019-04-30T01:36:45+00:00Z 2 particular, extensive results for thick beams with highly heterogeneous material lay-ups are discussed and compared with corresponding results obtained from elasticity solutions, two other "zigzag" theories, and high-fidelity finite element analyses. Comparisons with the baseline Timoshenko Beam Theory are also presented. The comparisons clearly show the improved accuracy of the new, refined "zigzag" theory presented herein over similar existing theories. This new theory can be readily extended to plate and shell structures, and should be useful for obtaining relatively low-cost, accurate estimates of structural response needed to design an important class of high-performance aerospace structures. KEYWORDS

The general linear equations governing the motion of moderately thick multilayered anisotropic shells are derived by making use of the principle of virtual work in conjunction with an a priori assumed displacement field. The assumed displacement field is piecewise linear in the u and v components and fulfills the static and geometric continuity conditions between the contiguous layers; furthermore, it takes into account the distortion of the deformed normal. Shear and rotatory inertia terms have also been considered in the formulation. Particularization of the resulting equations to the flat multilayered anisotropic plates is straightforward; thus, only the final expressions are given. The proposed approach gives, as particular cases, the linear equations of motion of the classical shells theory based on the Kirchhoff-Love kinematic hypothesis and those of the shear deformation theory for which it is assumed that the deformed normal do not distort.

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A refined zigzag theory is presented for laminated-composite and sandwich plates that includes the kinematics of first-order shear deformation theory as its baseline. The theory is variationally consistent and is derived from the virtual work principle. Novel piecewise-linear zigzag functions are used, providing a more realistic representation of the deformation states of transverse shear-flexible plates than other similar theories. The formulation does not enforce full continuity of the transverse shear stresses across the plate's thickness, yet it is robust. Transverse shear correction factors are not required to yield accurate results. The theory avoids the shortcomings of earlier zigzag theories (such as shearforce inconsistency and difficulties in simulating clamped boundary conditions) which have limited their accuracy. This new theory requires only C 0 -continuous kinematic approximations and is perfectly suited for developing computationally efficient finite elements. It should be useful for obtaining relatively efficient, accurate estimates of structural response, needed in designing high-performance load-bearing aerospace structures.A list of symbols can be found on page 363.