Investigation of mechanical responses of flexo-magnetic variable thickness nanoplates resting on elastic foundations, taking into account geometrical imperfections

This work utilizes the finite element approach together with an innovative shear strain theory to investigate the static bending behavior,free vibration features,and static buckling phenomena of flexo-magnetic nanoplates.The inquiry specifically examines the fluctuation in both the thickness of the plate and the elasticity of the foundation.The influence of initial geometrical imperfections,including several categories such as local and global faults,is also taken into account.The influences of several factors,including the law governing thickness fluctuation,types of imperfections,boundary conditions,and elastic foundation,on the mechanical response of the plate are considered.Outcomes of the work include new and original discoveries that have not been discussed in previous research,adding to both theoretical comprehension and practical implementation.

An isogeometric approach to free vibration analysis of bi-directional functionally graded porous doubly-curved shallow microshells with variable length-scale parameters

This study uses iso-geometric investigation,which is based on the non-uniform rational B-splines(NURBS)basis function,to investigate natural oscillation of bi-directional functionally graded porous(BFGP)doublycurved shallow microshells placed on Pasternak foundations with any boundary conditions.The characteristics of the present material vary in both thickness and axial directions along the x-axis.To be more specific,a material length-scale coefficient of the microshell varies in both thickness and length directions as the material's mechanical properties.One is able to develop a differential equation system with varying coefficients that regulate the motion of BFGP double-curved shallow microshells by using Hamilton principle,Kirchhoff-Love hypothesis,and modified couple stress theory.The numerical findings are reported for thin microshells that are spherical,cylindrical,and hyperbolic paraboloidal,with a variety of planforms,including rectangles and circles.The validity and effectiveness of the established model are shown by comparing the numerical results given by the proposed formulations with previously published findings in many specific circumstances.In addition,influences of length scale parameters,power-law indexes,thickness-to-side ratio,and radius ratio on natural oscillation responses of BFGP microshells are investigated in detail.