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

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.

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Shape sensing, i.e., reconstruction of the displacement field of a structure from surfacemeasured strains, has relevant implications for the monitoring, control and actuation of smart structures. The inverse finite element method (iFEM) is a shape-sensing methodology shown to be fast, accurate and robust. This paper aims to demonstrate that the recently presented iFEM for beam and frame structures is reliable when experimentally measured strains are used as input data. The theoretical framework of the methodology is first reviewed. Timoshenko beam theory is adopted, including stretching, bending, transverse shear and torsion deformation modes. The variational statement and its discretization with C 0-continuous inverse elements are briefly recalled. The three-dimensional displacement field of the beam structure is reconstructed under the condition that least-squares compatibility is guaranteed between the measured strains and those interpolated within the inverse elements. The experimental setup is then described. A thin-walled cantilevered beam is subjected to different static and dynamic loads. Measured surface strains are used as input data for shape sensing at first with a single inverse element. For the same test cases, convergence is also investigated using an increasing number of inverse elements. The iFEM-recovered deflections and twist rotations are then compared with those measured experimentally. The accuracy, convergence and robustness of the iFEM with respect to unavoidable measurement errors, due to strain sensor locations, measurement systems and geometry imperfections, are demonstrated for both static and dynamic loadings.

The paper presents a comparison between two existing zigzag functions that are used to improve equivalent single layer (ESL) theories for the analysis of multilayered composite and sandwich beams. ESL theories are easy to implement and computationally affordable but, in order to correctly describe the mechanical behavior of laminated structures (especially those exhibiting high transverse anisotropy or high thickness-to-side length ratios), the displacement field needs to be enriched by a through-the-thickness piecewise linear contribution denoted as "zigzag." The zigzag term of the displacement field is used to model the local distortion of the cross section in each lamina of multilayered structures and is related to the continuity of transverse stresses. The paper considers two zigzag functions that have been proposed in the open literature (namely Murakami's zigzag function and the refined zigzag function) and compares their performances when they are used to improve the classical Timoshenko beam theory; both displacement-based and mixed formulations are considered. To the best ofthe author's knowledge, such a comparative study has never been published. The problem of a simply supported beam subjected to a transverse distributed load is considered as a test case. Several stacking sequences, ranging from monolithic to sandwich-like and from symmetric to arbitrary, are considered. The special case of laminates with external weak layers is also investigated and the effects of these lay-ups on the derivation of the refined zigzag function are analyzed for the first time. The capability of the tested zigzag functions to help evaluate the overall deflection and model the through-the-thickness distribution of the axial displacement and stress is investigated. It has been recognized that the refined zigzag function is more accurate, especially for unsymmetric and arbitrary lay-ups and can be adopted to efficiently introduce zigzag kinematics into any ESL theory. 12 20 Pagano RZT-Mix (%E) Mur-Mix (%E) RZT-Dis (%E) Mur-Dis (%E) Pagano RZT-Mix (%E) Mur-Mix (%E) RZT-Dis (%E) Mur-Dis (%E) Pagano RZT-Mix (%E) Mur-Mix (%E) RZT-Dis (%E) Mur-Dis (%E) «MAX «NUN LI2h Model 1 = +h 2 = ~h 2 = -(4) 14 34 Pagano RZT-Mix {%E) Mur-Mix (%E) RZT-Dis (%E) Mur-Dis (%E) Pagano RZT-Mix (%E) Mur-Mix (%E) RZT-Dis (%E) Mur-Dis (%E) Pagano RZT-Mix (%E) Mur-Mix (%E) RZT-Dis (%E) Mur-Dis (%E)

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