Meaning
Non-linear elastic plate formulations extend classical thin plate theory to account for mid-plane stretching strains during moderate transverse deflection. Applying Von Karman plate theory allows structural engineers to predict bending stresses and membrane forces in thin battery pack housing covers and module end plates under internal expansion loads. Equations couple out-of-plane flexure with in-plane membrane stretching when plate displacement exceeds roughly half the plate thickness.
The mathematical model applies to thin structural plates undergoing moderate deflections, stopping where large strain elastoplastic behavior dominates structural response.
Strain Coupling
Mathematical differential equations balance lateral pressure loads against combined flexural rigidity and membrane tension. Under Von Karman plate theory, mid-surface strain terms incorporate squared gradient derivatives of transverse displacement. This mathematical coupling captures membrane stiffening, where plate deflection increases in-plane tensile stress and increases resistance to further bending.
Finite element solvers use these non-linear stress formulations to calculate accurate plate deformation profiles under swelling pressure.
Governing Equation
Coupled biharmonic equations solve simultaneously for Airy stress functions and lateral displacement fields under specified edge boundary conditions.
Enclosure Modeling
Battery structural design uses plate theory formulations to evaluate thin enclosure panel deformation without performing computationally expensive solid element modeling. Utilizing Von Karman plate theory optimizes wall thickness selection for lightweight battery enclosures while ensuring structural deflection limits remain satisfied.
