1,721,023 research outputs found
A robust and consistent first-order zigzag theory for multilayered beams
No full textIn this paper a recently developed refined first-order zigzag theory for multilayered beams is reviewed from a fresh theoretical perspective. The theory includes the kinematics of Timoshenko beam theory as its baseline. The use of a novel piecewise-linear zigzag function provides a more realistic representation of the deformation states of transverse-shear-flexible multilayered beams. Though the formulation does not enforce full continuity of the transverse-shear stresses across the beam’s depth, yet it is robust in the sense that transverse-shear correction factors are not required to yield accurate results. The new theory is variationally consistent, requires only C0-continuity for kinematic approximations, and is thus perfectly suited for developing computationally efficient finite elements
A consistent refinement of first-order shear-deformation theory for laminated composite and sandwich plates using improved zigzag kinematics
No full textA 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 that provide a more realistic representation of the deformation states of transverse-shear-flexible plates than other similar theories are used. The formulation does not enforce full continuity of the transverse shear stresses across the plate's thickness, yet is robust. Transverse-shear correction factors are not required to yield accurate results. The theory is devoid of the shortcomings inherent in the previous zigzag theories including shear-force inconsistency and difficulties in simulating clamped boundary conditions, which have greatly limited the accuracy of these theories. This new theory requires only C0-continuous kinematic approximations and is perfectly suited for developing computationally efficient finite elements. The theory should be useful for obtaining relatively efficient, accurate estimates of structural response needed to design high-performance load-bearing aerospace structure
A shear-deformation theory for composite and sandwich plates using improved zigzag kinematics
No full textRefined Zigzag Theory for Laminated Composite and Sandwich Plates
No full textA 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 that provide a more realistic representation of the deformation states of transverse-shear-flexible plates than other similar theories are used. The formulation does not enforce full continuity of the transverse shear stresses across the plate’s thickness, yet is robust. Transverse-shear correction factors are not required to yield accurate results. The theory is devoid of the shortcomings inherent in the previous zigzag theories including shear-force inconsistency and difficulties in simulating clamped boundary conditions, which have greatly limited the accuracy of these theories. This new theory requires only C0-continuous kinematic approximations and is perfectly suited for developing computationally efficient finite elements. The theory should be useful for obtaining relatively efficient, accurate estimates of structural response needed to design high-performance load-bearing aerospace structures
Refined zigzag theory for homogeneous, laminated composite, and sandwich plates: a homogeneous limit methodology for zigzag function selection
No full textThe Refined Zigzag Theory (RZT) for homogeneous, laminated composite, and sandwich plates is revisited to offer a fresh insight into its fundamental assumptions and practical possibilities. The theory is introduced from a multi-scale formalism starting with the in plane displacement field expressed as a superposition of coarse and fine contributions. The coarse displacement field is that of first-order shear deformation theory, whereas the fine displacement field has a piecewise linear zigzag distribution through the thickness. The resulting (cinematic field provides a more realistic representation of the deformation states of transverse-shear-flexible plates than other similar theories. The condition of limiting homogeneity of transverse-shear properties is proposed and yields four distinct sets of zigzag functions. Analytic solutions for highly heterogeneous sandwich plates undergoing elasto-static deformations are used to identify the best performing zigzag functions. Unlike previously used methods, which often result in anomalous conditions and nonphysical solutions, the present theory does not rely on transverse-shear-stress equilibrium constraints. For all material systems, there are no requirements for use of transverse-shear correction factors to yield accurate results. To model homogeneous plates with the frill power of zigzag kinematics, infinitesimally small perturbations in the transverse shear properties are derived, thus enabling highly accurate predictions of homogeneous plate behavior without the use of shear correction factors. The RZT predictive capabilities to model highly heterogeneous sandwich plates are critically assessed, demonstrating its superior efficiency, accuracy, and a wide range of applicability. The present theory, which is derived from the virtual work principle, is well-suited for developing computationally efficient C°-continuous finite elements, and is thus appropriate for the analysis and design of high performance load-bearing aerospace structures
Refinement of Timoshenko Beam Theory for Composite and Sandwich Beams using Zigzag Kinematics
No full textA 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 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
A refined zigzag beam theory for composite and sandwich beams
No full textA 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 subject to static loads are derived and the improved modelling capability of the new `zigzag' beam theory is demonstrated. In 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
A homogeneous limit methodology and refinements of computationally efficient zigzag theory for homogeneous, laminated composite, and sandwich plates
Full text linkThe Refined Zigzag Theory (RZT) for homogeneous, laminated composite, and sandwich plates is revisited to offer a fresh insight into its fundamental assumptions and practical possibilities. The theory is introduced from a multiscale formalism starting with the inplane displacement field expressed as a superposition of coarse and fine contributions. The coarse displacement field is that of first-order shear-deformation theory, whereas the fine displacement field has a piecewise-linear zigzag distribution through the thickness. The resulting kinematic field provides a more realistic representation of the deformation states of transverse-shear-flexible plates than other similar theories. The condition of limiting homogeneity of transverse-shear properties is proposed and yields four distinct variants of zigzag functions. Analytic solutions for highly heterogeneous sandwich plates undergoing elastostatic deformations are used to identify the best-performing zigzag functions. Unlike previously used methods, which often result in anomalous conditions and nonphysical solutions, the present theory does not rely on transverse-shear-stress equilibrium constraints. For all material systems, there are no requirements for use of transverse-shear correction factors to yield accurate results. To model homogeneous plates with the full power of zigzag kinematics, infinitesimally small perturbations in the transverse shear properties are derived, thus enabling highly accurate predictions of homogeneous-plate behavior without the use of shear correction factors. The RZT predictive capabilities to model highly heterogeneous sandwich plates are critically assessed, demonstrating its superior efficiency, accuracy, and a wide range of applicability. This theory, which is derived from the virtual work principle, is well-suited for developing computationally efficient, C0 a continuous function of (x1,x2) coordinates whose first-order derivatives are discontinuous along finite element interfaces and is thus appropriate for the analysis and design of high-performance load-bearing aerospace structures
A robust four-node quadrilateral element for laminated composite and sandwich plates based on Refined Zigzag Theory
Full text linkThe paper presents a locking-free four-node element for laminated composite and sandwich plates based on Refined Zigzag Theory (RZT). Initially, two RZT-based plate elements are derived using four-node and eight-node configurations, achieved by way of standard C0 isoparametric shape functions. In addition, with a view on improving the modelling of extremely thin plates, an anisoparametric four-node element is developed in which the transverse deflection variable is interpolated using quadratic polynomial shape functions, whereas the remaining kinematic variables are bilinear. A straightforward transverse-shear edge-constraint procedure gives rise to a four-node anisoparametric element. A further enhancement is achieved using an Element Shear Correction (ESC) factor that is derived from a strain-energy matching procedure. The resulting four-node element (ZQ4c) uses full Gauss quadrature, consistent load vector, and mass matrix. Furthermore, the ZQ4c stiffness matrix has no spurious zero-energy modes, and the element is extremely robust when modelling ultra-thin plates. Several numerical studies are carried out to demonstrate the predictive capabilities of the four elements examined in this investigation. It is concluded ZQ4c is a highly accurate element over a wide range of material systems and span-to-thickness ratios, and is the best performing element of the four elements examined in this study
A refined linear zigzag theory for composite beams: reformulation of zigzag function and shear stress constraints
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