Some Inconsistencies in the Nonlinear Buckling Plate Theories-FSDT, S-FSDT, HSDT

Area of Science:

• Solid Mechanics
• Structural Engineering
• Composite Materials

Background:

• Analyzing transverse forces in plates is essential for structural integrity.
• Existing theories like Classical Plate Theory (CPT) and First-Order Shear Deformation Theory (FSDT) have limitations.
• Understanding the interplay of bending and membrane forces is critical for thin-walled structures.

Purpose of the Study:

• To establish bending and membrane components of transverse forces in a fixed square isotropic plate.
• To investigate these forces under simultaneous compression and transverse loading.
• To propose a new formulation for nonlinear problems in thin-walled plate mechanics.

Main Methods:

• Utilized First-Order Shear Deformation Theory (FSDT), Simple First-Order Shear Deformation Theory (S-FSDT), and Classical Plate Theory (CPT).
• Employed a variational approach to formulate a new differential equation of equilibrium.
• Differentiated between transverse deformations accompanying bending components and those absent in membrane components.

Main Results:

• Established bending and membrane force components under combined loading conditions.
• Demonstrated that membrane components do not involve transverse deformations, implying transverse rigidity.
• Identified a specific range for considering membrane components in total transverse forces for nonlinear problems.

Conclusions:

• The proposed variational approach offers a new formulation for analyzing transverse forces in plates.
• The findings are particularly significant for the design and analysis of modern composite structures.
• Distinguishing between bending and membrane force contributions enhances the understanding of plate behavior under complex loading.