Effect of Curvilinear Reinforcing Fibers on the Linear Static Behavior of Soft-Core Sandwich Structures

Abstract

The present research deals with the linear static behavior of soft-core sandwich plates and shells. The external skins are reinforced by curvilinear fibers. Their curved paths are described by a general mathematical law that allows the definition of arbitrary placements. The mechanical behavior of these structures is modeled through several Higher-order Shear Deformation Theories (HSDTs) including the zig-zag effect, based on an Equivalent Single Layer (ESL) approach. The solution of the governing equations is achieved numerically by means of the Generalized Differential Quadrature (GDQ) method. A huge number of parametric investigations is proposed in graphical and tabular forms to highlight the influence of the fiber orientation on the static response. The results prove that the structural behavior is affected by such parameters. Thus, the desired structural behavior can be modified by means of a proper choice of the fiber orientation. was investigated by Gürdal and Olmedo [60] to evaluate the stiffness variation effect on the elastic response of the structure. In their work, the orientation of the fibers was defined by two parameters, which consisted of the fiber angle at the center of the laminate and the fiber angle at a specified distance from the center. The manufacturing process of the proposed approach was progressively studied by Waldarth et al. [61], Setoodeh and Gürdal [62], and Setoodeh et al. [63,64]. Jegley et al. [65] proved that the load carrying capability of panels reinforced by curvilinear fibers was superior to the one that characterized panels with straight fibers. Analogously, the stress concentrations around the hole were reduced due to the curvilinear paths of the fibers. Abdalla et al. [66] developed a maximization procedure for the natural frequency of composite panels reinforced by curved fibers. The post-buckling progressive damage behavior and the structural failure of variable-stiffness composite panels were studied by Lopes et al. [67] taking into account the residual thermal stresses caused by the curing process. Gürdal et al. [68] investigated the in-plane and buckling responses of flat rectangular composite laminates with variable stiffness. Their research proved that it was possible to vary either the buckling load or the in-plane stiffness of the structure. The variable-stiffness concept and the two-parameter law for the fiber orientation were extended also to conical and cylindrical shells by Blom et al. [69-71]. Akhavan and Ribeiro [72] investigated the natural frequencies and vibrational modes of variable-stiffness laminated composite plates reinforced by curvilinear fibers by means of a p-version finite element approach. The same topic was analyzed also by Honda and Narita [73], who proposed an analytical method for this purpose. Díaz et al. [74] presented a numerical method for obtaining the interlaminar stresses in variable stiffness composite panels. Coburn et al. [75] highlighted the improved buckling performances of variable-stiffness laminates compared to the ones re...

Isogeometric static analysis of laminated plates with curvilinear fibers based on Refined Zigzag Theory

“…14 that the transverse shear stress solutions of IG-RZT and ANSYS have matched perfectly for each four cases. However, the τ xz results of [45] for Case b3 and b4 have a slight discrepancy between IG-RZT and ANSYS. Hence, in the light of these results, the advantages of using IG-RZT formulation for 3-D stress analysis is further validated with respect to a continuum model and shown as compared to reference [45].…”

“…To further assess the accuracy of the present IG-RZT formulation, the bending analysis of a three-layer sandwich plate problem (Case b) from Tornabene and Bacciocchi [45] has been revisited. This sandwich structure is a square plate a ¼ b ¼ 1:5 m ð Þ subjected to a uniform pressure, q z ðz ¼ hÞ ¼ À10 kPa ½ with clamped boundary conditions on its all edges.…”

“…Fig. 13 shows the comparisons of through the thickness in-plane stresses obtained from IG-RZT analysis and the solutions of ANSYS and Tornabene and Bacciochi's approach [45] in which several thickness expansion terms are added into the displacement fields in addition to Murakami's zigzag functions. This ESL approach just as in [47] uses the differential quadrature method to solve the governing equations.…”

“…This ESL approach just as in [47] uses the differential quadrature method to solve the governing equations. The present IG-RZT results have been compared with EDZ4 of [45] which stands for (E)SL-(D)isplacement-Zigzag-Fourth order thickness expansion. For a clear comparison among the established case studies, graphs are divided into two parts: the results for (1) Case b1 and b3, and (2) Case b2 and b4.…”

“…For the structural analysis of curvilinear fiber laminated composites, various numerical methods such as finite element, boundary ele-ment, smoothed finite element, mesh-free, differential quadrature etc. [40][41][42][43][44][45][46][47] can be applied in the case of insufficient analytical solutions. Among these numerical approaches, finite element method (FEM) is a well-known one and frequently used in computer aided engineering industry (CAE).…”