Nonlinear finite element analysis of lattice core sandwich plates

TL;DR

This paper develops a nonlinear finite element model for lattice core sandwich plates using a 2-D micropolar plate theory, enabling efficient analysis of nonlinear bending and vibrations with good accuracy compared to 3-D models.

Contribution

It introduces a novel 2-D finite element model for lattice core sandwich panels that captures nonlinear behavior and boundary conditions efficiently, matching 3-D results with significantly reduced computational cost.

Findings

The 2-D model accurately predicts nonlinear bending and vibrations.

The model reduces computational cost by two orders of magnitude compared to 3-D models.

Good agreement with detailed 3-D FE results validates the approach.

Abstract

A displacement-based, geometrically nonlinear finite element model is developed for lattice core sandwich panels modeled as 2-D equivalent single-layer (ESL), first-order shear deformation theory (FSDT) micropolar plates. The nonlinearity is due to the moderate macrorotations of the plate which are modeled by including the von Karman strains in the micropolar strain measures. Weak form Galerkin method with linear Lagrange interpolations is used to develop the displacement-based finite element model. Selective reduced integration is used to eliminate shear locking and membrane locking. The novel finite element model is used to study the nonlinear bending and linear free vibrations of web-core and pyramid core sandwich panels. Clamped and free edge boundary conditions are considered for the first time for the 2-D micropolar ESL-FSDT plate theory. The present 2-D finite element results are in good agreement with the corresponding detailed 3-D FE results for the lattice core sandwich panels. The 2-D element provides computationally cost-effective solutions; in a nonlinear bending example, the number of elements required for the 2-D micropolar plate is of the order 10^3, whereas for the corresponding 3-D model the order is 10^5.