C0 beam elements based on the Refined Zigzag Theory for multilayered composite and sandwich laminates

The paper deals with the development and computational assessment of three- and two-node beam finite elements based on the Refined Zigzag Theory (RZT) for the analysis of multilayered composite and sandwich beams. RZT is a recently proposed structural theory that accounts for the stretching, bending, and transverse shear deformations, and which provides substantial improvements over previously developed zigzag and higher-order theories. This new theory is analytically rigorous, variationally consistent, and computationally attractive. The theory is not affected by anomalies of most previous zigzag and higher-order theories, such as the vanishing of transverse shear stress and force at clamped boundaries. In contrast to Timoshenko theory, RZT does not employ shear correction factors to yield accurate results. From the computational mechanics perspective RZT requires C°-continuous shape functions and thus enables the development of efficient displacement-type finite elements. The focus of this paper is to explore several low-order beam finite elements that offer the best compromise between computational efficiency and accuracy. The initial attention is on the choice of shape functions that do not admit shear locking effects in slender beams. For this purpose, anisoparametric (aka interdependent) interpolations are adapted to approximate the four independent kinematic variables that are necessary to model the planar beam deformations. To achieve simple two-node elements, several types of constraint conditions are examined and corresponding deflection shape-functions are derived. It is recognized that the constraint condition requiring a constant variation of the transverse shear force gives rise to a remarkably accurate two-node beam element. The proposed elements and their predictive capabilities are assessed using several elastostatic example problems, where simply supported and cantilevered beams are analyzed over a range of lamination sequences, heterogeneous material properties, and slenderness ratios

A Multi-scale Refined Zigzag Theory for Multilayered Composite and Sandwich Plates with Improved Transverse Shear Stresses

The Refined Zigzag Theory (RZT) enables accurate predictions of the in-plane displacements, strains, and stresses. The transverse shear stresses obtained from constitutive equations are layer-wise constant. Although these transverse shear stresses are generally accurate in the average, layer-wise sense, they are nevertheless discontinuous at layer interfaces, and thus they violate the requisite interlaminar continuity of transverse stresses. Recently, Tessler applied Reissner's mixed variational theorem and RZT kinematic assumptions to derive an accurate and efficient shear-deformation theory for homogeneous, laminated composite, and sandwich beams, called RZT(m), where "m" stands for "mixed". Herein, the RZT(m) for beams is extended to plate analysis, where two alternative assumptions for the transverse shear stresses field are examined: the first follows Tessler's formulation, whereas the second is based on Murakami's polynomial approach. Results for elasto-static simply supported and cantilever plates demonstrate that Tessler's formulation results in a powerful and efficient structural theory that is well-suited for the analysis of multilayered composite and sandwich panels

A novel algorithm for shape parameter selection in radial basis functions collocation method

Many Radial Basis Functions (RBF) contain a free shape parameter that plays an important role for the application of meshless method to the analysis of multilayered composite and sandwich plates. In most papers the authors end up choosing this shape parameter by trial and error or some other ad-hoc means. In this paper a novel algorithm for shape parameter selection, based on a convergence analysis, is presented. The effectiveness of this algorithm is assessed by static analyses of laminated composite and sandwich plate

A Refined Zigzag Beam Theory for Composite and Sandwich Beams

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 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

COVID-19’s spatiotemporal patterns within cities: a global comparative study

The first confirmed cases of COVID-19 were discovered around the end of 2019 in Wuhan, Hubei Province, China, and the world as we knew it changed from then on. Whereas most of the research has focused on the meso-urban scale, there is only a limited number of studies focusing on the distribution of cases at a spatially granular scale within cities, throughout time. This work aims at filling this gap, by drawing different cities across the globe into a comparative project, where the spread of the pandemic is analysed throughout three distinct ‘waves’ of the pandemic. This study sheds light on the current debate about the variability of results across time and space, and how insights need to be reframed by accounting for the spatiotemporal dynamicity of COVID-19

Buckling and vibration analysis of laminated composite plate/shell structures via a smoothed quadrilateral flat shell element with in-plane rotations

This paper presents buckling and free vibration analysis of composite plate/shell structures of various shapes, modulus ratios, span-to-thickness ratios, boundary conditions and lay-up sequences via a novel smoothed quadrilateral flat element. The element is developed by incorporating a strain smoothing technique into a flat shell approach. As a result, the evaluation of membrane, bending and geometric stiffness matrices are based on integration along the boundary of smoothing elements, which leads to accurate numerical solutions even with badly-shaped elements. Numerical examples and comparison with other existing solutions show that the present element is efficient, accurate and free of locking

Beyond density: COVID-19 as an accelerator of spatial (in)justices

Around the end of 2019, in Wuhan, Hubei Province, China, the first confirmed cases of COVID-19 were identified, and from then on, the world we were used to knowing changed globally. The role of population density, in relation to the spread of the pandemic, has been widely scrutinised in urban studies, believed to be the triggering variable. However, the results so far are inconclusive. This paper suggests instead to shift the focus to socio-spatial vulnerabilities, as the effects of the pandemic's spread have been more severe in urban units which feature long-standing inequalities. The paper's aim is, therefore, twofold: on the one hand it aims at contributing to the debate on population density and COVID-19 in urban areas, and, on the other hand, to analyse the pandemic's spread in relation to socio-spatial vulnerabilities. Different cities across the globe are drawn into a comparative project, where the pandemic's spread is analysed in relation to variables of Population Density (PD) and a Social Vulnerability Index (SVI), by employing correlation matrices. The results suggest that there is no significant correlation between density and the spread of COVID-19. Instead, a positive correlation is in place when analysing the pandemic's diffusion with socio-spatial inequalities

First-order displacement-based zigzag theories for composite laminates and sandwich structures: a review

The paper gives a critical review and new accomplishments of the displacement based zigzag theories for laminated composite and sandwich structures, with special emphasis to the underlying ideas, relative strengths and weakneses. Some numerical results substantiate the conclusiones

Zigzag theories for composite laminates and sandwich structures

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