Free vibration and dynamic response of sandwich composite plates with auxetic honeycomb core

This paper deals with the free vibration and dynamic responses of composite sandwich plates. The sandwich plate has three layers in which two face sheets are made of isotropic material, and the core layer is made of auxetic honeycomb structures with a negative Poisson's ratio. A smoothed finite element model based on the first-order shear deformation theory is established for the analysis purpose. In the model, only the linear approximation is necessary, and the discrete shear gap method for triangular plate elements is used to avoid the shear locking. The Newmark direct integration technique is used to capture the dynamic responses of the sandwich plates. The convergence study is made, and the accuracy of present results is validated by comparison with available data in the literature. The influence of geometrical parameters, material properties, and boundary conditions are explored and discussed. Numerical results show that auxetic materials have several different responses compared to conventional materials, and these behaviors are strongly influenced by the internal structure of the auxetic material.

A 4-node quadrilateral element with center-point based discrete shear gap (CP-DSG4)

This work aims at presenting a novel four-node quadrilateral element, which is enhanced by integrating with discrete shear gap (DSG), for analysis of Reissner-Mindlin plates. In contrast to previous studies that are mainly based on three-node triangular elements, here we, for the first time, extend the DSG to four-node quadrilateral elements. We further integrate the fictitious point located at the center of element into the present formulation to eliminate the so-called anisotropy, leading to a simplified and efficient calculation of DSG, and that enhancement results in a novel approach named as "four-node quadrilateral element with center-point based discrete shear gap - CP-DSG4". The accuracy and efficiency of the CP-DSG4 are demonstrated through our numerical experiment, and its computed results are validated against those derived from the three-node triangular element using DSG, and other existing reference solutions.

A Gradient Stable Node-Based Smoothed Discrete Shear Gap Method for Analysis of Reissner–Mindlin Plates

In this paper, a gradient stable node-based smoothed discrete shear gap method (GS-DSG) using 3-node triangular elements is presented for Reissner–Mindlin plates in elastic-static, free vibration, and buckling analyses fields. By applying the smoothed Galerkin weak form, the discretized system equations are obtained. In order to carry out the smoothing operation and numerical integration, the smoothing domain associated with each node is defined. The modified smoothed strain with gradient information is derived from the Hu–Washizu three-field variational principle, resulting in the stabilization terms in the system equations. The stabilized discrete shear gap method is also applied to avoid transverse shear-locking problem. Several numerical examples are provided to illustrate the accuracy and effectiveness. The results demonstrate that the presented method is free of shear locking and can overcome the temporal instability issues, simultaneously obtaining excellent solutions.

Static and Free Vibration Analyses of Functionally Graded Carbon Nanotube Reinforced Composite Plates using CS-DSG3

This study presents an extension of the cell-based smoothed discrete shear gap method (CS-DSG3) using three-node triangular elements for the static and free vibration analyses of carbon nanotube reinforced composite (CNTRC) plates. The single-walled carbon nanotubes (SWCNTs) are assumed to be uniformly distributed (UD) and functionally graded (FG) distributed along the thickness direction. The material properties of carbon nanotube-reinforced composite plates are estimated according to the rule of mixture. The governing equations are developed based on the first-order shear deformation plate theory (FSDT). In the CS-DSG3, each triangular element will be divided into three sub-triangles, and in each sub-triangle, the stabilized discrete shear gap method is used to compute the strains and to avoid the transverse shear locking. Then the strain smoothing technique on the whole triangular element is used to smooth the strains on these three sub-triangles. Effects of several parameters, such as the different distribution of carbon nanotubes (CNTs), nanotube volume fraction, boundary condition and width-to-thickness ratio of plates are investigated. In addition, the effect of various orientation angles of CNTs is also examined in detail. The accuracy and reliability of the proposed method are verified by comparing its numerical solutions with those of other available results in the literature.

ABAQUS IMPLEMENTATION OF A COROTATIONAL PIEZOELECTRIC 3-NODE SHELL ELEMENT WITH DRILLING DEGREE OF FREEDOM

Integration of classical, passive structures and active elements based on multi-functional materials resulted in a novel structural concept denoted as active structures. The new structural systems are characterized by self-sensing and actuation. Coupling the two distinctive features by means of a controller enables a number of exquisite functionalities such as vibration suppression, noise attenuation, shape control, structural health monitoring, etc. Reliable, accurate and highly efficient modeling tools are an important ingredient of the active structure design. This paper addresses the Abaqus implementation of a recently developed piezoelectric 3-node shell element. The element uses co-rotational formulation to cover geometric nonlinearities. Special techniques are used to address the issues originating from low-order interpolation functions. The discrete shear gap is used to resolve the shear locking, while the assumed natural deviatoric strain technique improves the membrane behavior. Examples are computed in Abaqus upon implementation of the developed element.

An Edge-Based Smoothed Discrete Shear Gap Method for Static and Free Vibration Analyses of FG-CNTRC Plates

In this paper, an edge-based smoothed stabilized discrete shear gap method (ES-DSG) is integrated with the C0-type high-order shear deformation plate theory (C0-HSDT) for free vibration and static analyses of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates. The material properties of FG-CNTRC are assumed to be graded through the thickness direction according to several distributions of the volume fraction of carbon nanotubes (CNTs). The stiffness formulation of the ES-DSG based on C0-HSDT is performed by using the strain smoothing technique over the smoothing domains associated with edges of elements. This hence does not require shear correction factors. The accuracy and reliability of the proposed method are confirmed in several numerical examples.

Stochastic Vibration Analysis of Functionally Graded Plates with Material Randomness Using Cell-Based Smoothed Discrete Shear Gap Method

A cell-based smoothed finite element method with discrete shear gap technique is used to study the stochastic free vibration behavior of functionally graded plates with material uncertainty. The plate kinematics is based on the first-order shear deformation theory and the effective material properties are estimated by simple rule of mixtures. The input random field is represented by the Karhunen–Loéve expansion and the polynomial chaos expansion is used to represent the stochastic output response. The accuracy of the proposed approach in terms of the first- and the second-order statistical moments are demonstrated by comparing the results with the Monte Carlo Simulations. A systematic parametric study is carried out to bring out the influence of the material gradient index, the plate aspect ratio and the skewness of the plate on the stochastic global response of functionally graded plates. It is inferred that all the considered parameters significantly influence the statistical moments of the first fundamental mode.

Analysis of static and free vibration of the sandwich folded plate using the Layerwise theory

In this paper, the static and free vibration analyses of the sandwich folded plate modeled by layer-wise (LW) theory are studied. In the theory, the continuity displacement condition is imposed at the layer’s interfaces. Each layer of the plate is modeled by the first-order shear deformation theory (FSDT). The numerical solutions are obtained by using the cellbased smoothed discrete shear gap method (CS-DSG3). Some examples are implemented to demonstrate the accuracy of the LW theory for the sandwich folded plate analyses.