Wrinkling Analysis of Double Nanofilms Embedded in Compliant Substrates Based on Nonlocal Elasticity Theory

In this paper, an analytical approach for wrinkling analysis of double nanofilms embedded in compliant substrates is presented. The governing differential equations for wrinkling of double nanofilms are derived based on Eringen’s nonlocal elasticity theory and the classical plate theory (CLPT). Substrates are regarded as elastic bodies of finite thickness and the normal pressure of substrates on the films is assumed to be linear with the lateral deformation of the films. Solutions for critical wrinkling load and wave number are computed in terms of the nonlocal parameter, the elastic properties and thickness of double nanofilms, the elastic properties and thickness of the substrates, and wrinkle modes. The parametric study shows that the dimensionless critical wave number and the dimensionless critical load decrease gradually with the increase of the nonlocal parameter. Four typical wrinkling states are studied: in-phase wrinkling, out-of-phase wrinkling, single-film wrinkling and asymmetric wrinkling. In-phase wrinkling has the highest chance to occur among four wrinkle modes. In addition, the results show that the dimensionless critical load and wave number are much smaller when the films become much stiffer and thinner than the substrates.

Investigation on material combination technique to enhance the anti-wrinkle and anti-vibration characteristics of the planar membrane reflector

In recent trends, membrane structure has increased its applications in space missions due to its significant advantages, such as light in weight, higher folding and packaging efficiency, ease of deployment, and low on-Board volume requirement. The wrinkling and low natural frequency of vibration are the major problems with the membrane structure. This research presents a novel methodology of Kapton-Kevlar material combination for a planar membrane reflector to enhance anti-vibration and anti-wrinkling capabilities of the membrane structure. The comparative study is made for the wrinkle area, RMS error, and natural frequency of vibration with the employed approach. This study provides new insights into a material combination technique to increase performance characteristics of the space-borne membrane reflectors. The outcome of the wrinkling analysis is compared and found to be consistent with the method available in the literature. From the simulation results, it is observed that wrinkles are reduced, and the natural frequency of vibration is also increased significantly with the proposed method.

Wrinkling Analysis of Pre-Stressed Rectangular Membranes Using Element-Free Galerkin Method

In this study, element-free Galerkin method (EFGM), a meshless method, is proposed for wrinkling analysis of pre-stressed rectangular membranes. The mathematical model for studying wrinkling of pre-stressed membranes is derived by considering the bending stiffness, though it is negligible. Moving least-square approximation for deflection is constructed by considering three degrees of freedom per node. Essential boundary conditions are imposed using scaled transformation matrix method. Initially, compression-induced buckling of a homogeneous thin plate without pre-stress is solved to validate the method and then a pre-stressed homogeneous membrane is analyzed for both compression-induced and shear-induced wrinkling. Capabilities of the proposed method for membrane analysis are compared with that of the finite element method (FEM). Comparative study on wrinkling analysis using EFGM and different FEM element types in a commercial FEM package shows that in lower modes both methods show satisfying consistency in eigenvalues with respect to the total of number of nodes, while at higher modes EFGM shows better consistency than FEM. Further, the study is extended to wrinkling of nonhomogeneous membranes subjected to linearly-varying in-plane load. The results obtained from EFGM analysis is compared and found to be matching well with those available in the literature.