A high-order finite element continuation for buckling analysis of porous FGM plates

Radial point interpolation‐Chebychev method with asymptotic numerical method for nonlinear buckling analysis of graphene oxide powder‐reinforced composite beams

“…The parameter 𝜖 serves as the control parameter, similar to Newton-Raphson algorithms, and can be determined using some parametrization techniques. 28,29 In the current study, the definition of 𝜖 is selected by projecting the increment as follows:…”

“…This could mean, for example, a transition from a stable equilibrium to an unstable one, or the emergence of new oscillatory behavior. 20,22,23,29,[31][32][33][34][35][36][37][38][39][40] Bifurcation analysis has applications in many areas of science and engineering. For example, in physics, bifurcation analysis can be used to understand the behavior of complex systems such as fluid flows.…”

“…$$ The subscripts 0 and $$$ k $$$ respectively indicate the starting and end branch solutions. The parameter $$$ \epsilon $$$ serves as the control parameter, similar to Newton‐Raphson algorithms, and can be determined using some parametrization techniques 28,29 . In the current study, the definition of $$$ \epsilon $$$ is selected by projecting the increment as follows: $$$$ \epsilon =<q-{q}_0>\left\{{q}_1\right\}+\left(\lambda -{\lambda}_0\right){\lambda}_1 $$$$ where $$$ <\bullet > $$$ is a transpose of $$$ \left\{\bullet \right\} $$$.…”

“…In particular, bifurcation analysis is concerned with identifying critical parameter values at which the behavior of the system undergoes a qualitative change. This could mean, for example, a transition from a stable equilibrium to an unstable one, or the emergence of new oscillatory behavior 20,22,23,29,31–40 . Bifurcation analysis has applications in many areas of science and engineering.…”

Nonlinear Vibration of Saturated Porous Functionally Graded Plate in Thermal Environment

“…Xue et al, [1] investigated the free vibration behaviors of ________ functionally graded porous cylindrical panels and shells by utilizing the first order shear deformation theory in conjunction with Hamilton's principle. Chaabani et al, [2] presented an effective approach to investigating the buckling and post-buckling behavior of porous FGM plates using higher order shear deformation theory. Further, He et al, [3] delved into the nonlinear vibration characteristics and response of a doubly curved shallow shell made of laminated carbon fiber reinforced resin, which had a porous microcapsule coating.…”