Two-scale micropolar plate model for web-core sandwich panels

Abstract

A 2-D micropolar equivalent single-layer (ESL), first-order shear deformation (FSDT) plate model for 3-D web-core sandwich panels is developed. First, a 3-D web-core unit cell is modeled by classical shell finite elements. A discrete-to-continuum transformation is applied to the microscale unit cell and its strain and kinetic energy densities are expressed in terms of the macroscale 2-D plate kinematics. The hyperelastic constitutive relations and the equations of motion (via Hamilton's principle) for the plate are derived by assuming energy equivalence between the 3-D unit cell and the 2-D plate. The Navier solution is developed for the 2-D micropolar ESL-FSDT plate model to study the bending, buckling, and free vibration of simply-supported web-core sandwich panels. In a line load bending problem, a 2-D classical ESL-FSDT plate model yields displacement errors of 34-175% for face sheet thicknesses of 2-10 mm compared to a 3-D FE solution, whereas the 2-D micropolar model gives only small errors of 2.7-3.4% as it can emulate the 3-D deformations better through non-classical antisymmetric shear behavior and local bending and twisting.

Post-buckling of web-core sandwich plates based on classical continuum mechanics: success and needs for non-classical formulations

“…The decrease is unphysical and can be corrected by incorporation nonclassical continuum mechanics assumptions into our FSDT-ESL model. As shown by Romanoff and Varsta [21], Jelovica and Romanoff [42] by thick-face plates sandwich theory and by Karttunen et al [36] by micropolar theory, the shear deformations of sandwich panels can have only finite wave-lengths, that is, finite n-values. When using thick-faces effect or micropolar solution, physically correct behavior is obtained.…”

“…It has been shown in Refs. [21,36] that non-local plate formulations are needed in the cases were the laserstake weld is assumed to be flexible or if l micro /l macroratio would be significantly larger. In cases where the l micro /l macro -ratio would be significantly smaller, the shear-induced stress fluctuations would be less important.…”

“…In terms of plates, it has been discussed by several authors(see, e.g., Refs. [1,3,4,[11][12][13][14][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]). In plates, the main idea is to reduce the mathematical [18]; full-scale ship collisions Ehlers et al [37] and quasi-static plate punch experiments Körgesaar et al [38]) description to Equivalent Single Layer (ESL) representation in which the deformations and stress resultants (forces and moments) are computed for known load and boundary conditions.…”

Nonlinear finite element analysis of lattice core sandwich plates

“…The matrices include 24 constitutive parameters and are symmetric in all cases in this study. The novel parameter values obtained for the pyramid core from the constitutive modeling process presented by Karttunen et al (2019) are given in Appendix B.…”

“…Detailed bending-dominated lattice unit cells may be constructed using beam and shell finite elements and the micropolar theory allows us to pass information related to both the translational and the rotational degrees of freedom of the beam and shell elements from a detailed FE model into, for example, a 2-D ESL plate model through a homogenization process. Recently Karttunen et al (2019) used the micropolar theory to model 3-D web-core sandwich panels as 2-D orthotropic equivalent-single layer first-order shear deformation (ESL-FSDT) micropolar plates. Linear transverse deflections and free linear vibrations of web-core lattice plate were considered by using the Navier solution for simply-supported plates.…”