https://northumbria-test.eprints-hosting.org/id/document/265204

A review of continuum mechanics models for size-dependent analysis of beams and plates

Localisation studies have been carried out for an unconstrained, elasto-plastic, strain-softening Cosserat continuum. Because of the presence of an internal length scale in this continuum model a perfect convergence is found upon mesh refinement. A finite, constant width of the localisation zone and a finite energy dissipation are computed under static as well as under transient loading conditions. Because of the existence of rotational degrees-of-freedom in a Cosserat continuum additional wave types arise and wave propagation becomes dispersive. This has been investigated analytically and numerically for an elastic Cosserat continuum and an excellent agreement has been found between both solutions.

Localisation in a Cosserat continuum under static and dynamic loading conditions

Literature related to recent work in predicting ultimate strength of a ship hull girder is reviewed and discussed. Instability factors are presented for determining the maximum load such a girder will sustain in the sagging mode. Two bibliography sections are included: one for ultimate load for box structures and the other for primary and secondary structure associated with ultimate strength.

Ultimate longitudinal strength

A novel three-variable shear deformation plate formulation: Theory and Isogeometric implementation

Mechanical properties of 3D double-U auxetic structures

Buckling and free vibration of shear-flexible sandwich beams using a couple-stress-based finite element

https://research.aalto.fi/files/39749173/ENG_Karttunen_et_al_Micropolar_modeling_approach_Composite_structures.pdf

Micropolar modeling approach for periodic sandwich beams

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

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 nonlinear strains in the micropolar strain measures. Weak-form Galerkin formulation with linear Lagrange interpolations is used to develop the displacement 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 1 0 3 , whereas for the corresponding 3-D model the order is 1 0 5 .

Nonlinear finite element analysis of lattice core sandwich plates

Constitutive equations are derived for a 1-D micropolar Timoshenko beam made of a web-core lattice material. First, a web-core unit cell is modeled by discrete classical constituents, i.e., the Euler–Bernoulli beam finite elements (FE). A discrete-to-continuum transformation is applied to the microscale unit cell and its strain energy density is expressed in terms of the macroscale 1-D beam kinematics. Then the constitutive equations for the micropolar web-core beam are derived assuming strain energy equivalence between the microscale unit cell and the macroscale beam. A micropolar beam FE model for static and dynamic problems is developed using a general solution of the beam equilibrium equations. A localization method for the calculation of periodic classical beam responses from micropolar results is given. The 1-D beam model is used in linear bending and vibration problems of 2-D web-core sandwich panels that have flexible joints. Localized 1-D results are shown to be in good agreement with experimental and 2-D FE beam frame results.

Anssi T. Karttunen

Papers

Buckling and free vibration of shear-flexible sandwich beams using a couple-stress-based finite element

Micropolar modeling approach for periodic sandwich beams

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

Nonlinear finite element analysis of lattice core sandwich plates

Two-scale constitutive modeling of a lattice core sandwich beam