The beam on elastic foundation is a general model used in physical, biological, and technological problems to study delamination, wrinkling, or pattern formation. Recent focus has been given to the buckling of beams deposited on liquid baths, and in the regime where the beam is soft compared to hydrostatic forces the wrinkling pattern observed at buckling has been shown to lead to localization ...

This paper is concerned with two issues that arise in the finite element analysis of 3D solids. The first issue examines the objectivity of various stress rates that are adopted in incremental analysis of solids. In doing so, it is revealed that large errors are incurred by an improper choice of stress rate. An example problem is presented to show the implications of the choice of stress rate. ...

Treated herein is the elastic buckling problem of Single-Walled Carbon Nanotubes (SCNTs) under axial compression. Critical buckling strains cr ε of stocky SCNTs (length/diameter less than 8) that have been obtained by modeling them as first-order shear deformation (thick) shell theory (FSDST). The buckling strains are compared with those obtained by commonly used thin shell theories, such as th...

This paper is devoted to the buckling analysis of thin composite plates under straight single-walled carbon nanotubes reinforcement with uniform distribution and random orientations. In order to develop the fundamental equations, the B3-Spline finite strip method along with the classical plate theory (CPT) is employed and the total potential energy is minimized which leads to an eigenvalue prob...

In present study, thermo-elastic buckling analysis of multi-layer orthotropic annular/circular graphene sheets is investigated based on Eringen’s theory. The moderately thick and also thick nano-plates are considered. Using the non-local first and third order shear deformation theories, the governing equations are derived. The van der Waals interaction between the layers is simulated for multi-...

The buckling behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates resting on Winkler-Pasternak elastic foundations under in-plane loads for various temperatures is investigated using element-free Galerkin (EFG) method based on first-order shear deformation theory (FSDT). The modified shear correction factor is used based on energy equivalence principle. Carbon ...

In this study, the buckling and free vibration of Timoshenko beams resting on variable elastic foundation analyzed by means of a new finite element formulation. The Winkler model has been applied for elastic foundation. A two-node element with four degrees of freedom is suggested for finite element formulation. Displacement and rotational fields are approximated by cubic and quadratic polynomia...

This paper deals with dynamic Stability of single walled carbon nanotube. Strain gradient theory and Euler-Bernouli beam theory are implemented to investigate the dynamic stability of SWCNT embedded in an elastic medium. The equations of motion were derived by Hamilton principle and non-local elasticity approach. The nonlocal parameter accounts for the small-size effects when dealing with nano-...

This work develops a framework for SIMP-based topology optimization of a metallic panel structure subjected to design-dependent aerodynamic, inertial, elastic, and thermal loads. Multi-physics eigenvalue-based design metrics such as thermal buckling and dynamic flutter are derived, along with their adjoint-based design derivatives. Locating the flutter point (Hopf-bifurcation) in a precise and ...

In this paper, we demonstrate how deformation patterns of leaves and fruits in growing and drying processes can be described via the inhomogeneous field theory. The distorted deformation of ribbed leaves and the ridge formation on fruit surfaces can be understood as the energy-minimizing mechanical buckling patterns. The swelling and de-swelling induced instabilities of various membrane structu...