Most of the phenomena of various fields of applied sciences are nonlinear problems. Recently, various types of analytical approximate solution techniques were introduced and successfully applied to the nonlinear differential equations. One of the aforementioned techniques is the Homotopy analysis method (HAM). In this study, we applied HAM to find critical buckling load of a column under end lo...

The buckling of hyperelastic incompressible cylindrical shells of arbitrary length and thickness under axial load is considered within the framework of nonlinear elasticity. Analytical and numerical methods for bifurcation are obtained using the Stroh formalism and the exact solution of Wilkes [Q. J. Mech. Appl. Math. 8:88–100, 1955] for the linearized problem. The main focus of this paper is t...

Lithographically defined electrical interconnects with thin, filamentary serpentine layouts have been widely explored for use in stretchable electronics supported by elastomeric substrates. We present a systematic and thorough study of buckling physics in such stretchable serpentine microstructures, and a strategic design of serpentine layout for ultra-stretchable electrode, via analytical mode...

We investigate the buckling of a slender rod embedded in a soft elastomeric matrix through a combination of experiments, numerics and theory. Depending on the control parameters, both planar wavy (2D) or non-planar coiled (3D) configurations are observed in the post-buckling regime. Our analytical and numerical results indicate that the rod buckles into 2D configurations when the compression fo...

We have studied the scaling of controlled nonlinear buckling processes in materials with dimensions in the molecular range (i.e., approximately 1 nm) through experimental and theoretical studies of buckling in individual single-wall carbon nanotubes on substrates of poly(dimethylsiloxane). The results show not only the ability to create and manipulate patterns of buckling at these molecular sca...

This paper describes an optimization procedure to design thermoplastic composite panels under axial compressive load conditions. Minimum weight is the goal. The panel design is subject to buckling constraints. The presence of the bending-twisting coupling and of particular boundary conditions does not allow an analytical solution for the critical buckling load. Surrogate models are used to appr...

This paper presents an analytical method to calculate the buckling stress of a rectangular thin plate under nonuniform applied axial stresses. Two cases are considered, buckling of a plate simply supported on all four sides and buckling of a plate simply supported on three sides with one unloaded edge free and the opposite unloaded edge rotationally restrained. These two cases illustrate the in...

A comparative study of different modeling approaches for predicting sandwich panel buckling response is described. The study considers sandwich panels with anisotropic face sheets and a very thick core. Results from conventional analytical solutions for sandwich panel overall buckling and face-sheet-wrinkling type modes are compared with solutions obtained using different finite element modelin...

An analytical study along with a numerical investigation is conducted to determine the lateral buckling strength of thin-walled open-section I shape composite beams. Based on Vlasov-type linear hypothesis beam stiffness coefficients, which account for a cross section geometry and material anisotropy of the section, are obtained. In this study the axial and bending coupling terms ( A,, , A,, , D...

An analytical investigation is conducted to predict the post-buckling strength of laminated composite stiffened panels under compressive loads. When a stiffened composite panel buckles, the skin would deform into a sinusoidal mode shape, and hence induces additional moments and forces near the skin-stiffener interface region. These induced loads would cause the existing small edge delamination ...