Through a set of comparative studies with 3D full-field models as references, the accuracy and efficacy of the proposed dimension reduction methodology are demonstrated for a diverse range of problem parameters for analyzing the large-amplitude dynamic structural response. A higher-order \(\)-continuous 6-node finite element is adopted for the discretization of the governing variational formulation with respect to the spatial domain, and an arc-length continuation technique along with time periodic discretization is implemented to solve the resulting nonlinear time-dependent problem.
Standard and higher-order computational homogenization methods determine the classical and strain gradient material constants, respectively. The corresponding governing equations follow Mindlin’s SG elasticity theory including the micro-inertia effect applied to the first-order shear deformation plate theory along with the nonlinear von Kármán kinematics. The proposed model based on the nonlinear finite element strain gradient elasticity is developed for the first time to provide a computationally efficient framework for the simulation of the underlying nonlinear dynamics of cellular plates with advanced microarchitectures.
The main objective of this paper is to develop a theoretically and numerically reliable and efficient methodology based on combining a finite element method and a strain gradient shear deformation plate model accounting for the nonlinear free and forced vibrations of cellular plates having equitriangularly prismatic metamaterial cores. in, with the corresponding kinematic formulations for both thin and thick structures and with isogeometric analysis for numerical solutions. SGT-based theoretical studies on the structural analysis and the determination of higher-order constitutive parameters of cellular beams and plates with prismatic cores have been reported by Khakalo et al. Closely connected to the present study, micropolar plate models were adopted in to present a 2D equivalent singlelayer for lattice core sandwich plates and panels, and the resulting problem was solved by linear Lagrange interpolation finite elements along with the selective reduced integration approach. Since solids with different microarchitectures under various loading conditions and deformation states might not be appropriately modeled by using a unified generalized continuum theory, different models such as the Cosserat theory, micropolar theory and higher gradient theories 44,45, have been developed. Inhalation of toxic dust (crystalline silica, asbestos, lead paint and other toxins) can lead to serious or fatal disease (silicosis, asbestos, lead or other poisoning).DO NOT USE abrasives containing more than one percent crystalline (free) silica.Blast operators and others working in the vicinity of abrasive blasting must wear properly-maintained, NIOSH-approved, respiratory protection appropriate for the job site hazards.Requires 6-25 CFM air supply and 60-125 psi working pressure for optimal performance.6" wheels and convenient handle for easy mobility.Includes (4) interchangeable ceramic nozzles: 2.0, 2.5, 3.0 & 3.5mm.
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