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

• Published in: International journal of solids and structures Vol. 170; pp. 82 - 94
• Main Authors: Karttunen, Anssi T., Reddy, J.N., Romanoff, Jani
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01-10-2019; Elsevier BV
• Subjects: Antisymmetric shear; Constitutive modeling; Constitutive relationships; Equations of motion; Equivalence; Free vibration; Kinematics; Kinetic energy; Local bending and twisting; Magma; Micropolar plate; Navier solution; Sandwich panels; Sandwich structures; Shear deformation; Three dimensional models; Twisting; Two dimensional models; Unit cell; Webs; Micropolar plate; Navier solution; Local bending and twisting; Sandwich structures; Antisymmetric shear; Constitutive modeling
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/j.ijsolstr.2019.04.026

•2-D micropolar plate model is developed for 3-D web-core sandwich panels.•The micropolar formulation is built upon on two-scale constitutive modeling.•A classical 3-D unit cell represents the microscale and the 2-D plate the macroscale.•Navier solution is derived for the novel 2-D micropolar plate model.•Problems unsolvable by classical plates are solved by the micropolar one.
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.