Finite strip elements for laminated composite plates with transverse shear strain discontinuities

This paper presents accurate inter-lamina stress distributions of laminated composite annular disks incorporating layer-wise zig-zag theory. This theory is based on the superposition of a global higher order shear deformation displacement field and a local linear zig-zag displacement field (RHOT). RHOT automatically satisfies displacement continuity at the layer interfaces and by further application of stress continuity at the layer interfaces and traction free boundary conditions, the unknown degrees of freedom are reduced to seven regardless of the number of layers. These are two in-plane displacements, two shear rotations, a transverse displacement and two section rotations. A four-node sector finite element in a cylindrical coordinate system is developed using RHOT. Two in-plane displacements and two shear rotations which are C0 continuous are interpolated using bilinear functions and a transverse displacement and two section rotations which are C1 continuous are interpolated using higher order Hermitian functions. In-plane normal stress and inter-lamina transverse shear stress variation through the thickness are calculated for laminated disks using a RHOT sector element and comparison is made with first order shear deformation theory predictions. The present work precedes the application of the zig-zag theory to transient dynamic analysis and is a first step at establishing the accuracy of implementing the zig-zag theory into a sector finite element.

A microstructure-based model for a full lamellar-interlamellar displacement and shear strain mapping inside human intervertebral disc core

In this paper, an accurate and efficient C0-type third-order global---local model incorporating effects of the transverse normal strain is proposed to study the thermal/mechanical behaviors of thick multilayer cross-ply plates. Transverse displacement is assumed to be a linear distribution through the thickness direction, for which the normal strain could be readily computed. Based on the interlaminar continuity conditions of in-plane displacement and transverse shear stresses, layer-dependent variables could be reduced. Employing shear stress free condition at the upper and the lower surfaces, derivatives of transverse displacement are eliminated from the displacement field, so that C0 interpolation functions are only required for the finite element implementation. As a result, the number of variables is independent of the number of layers of the laminate. To assess the proposed model, the classical quadratic eight-node isoparametric element is used for the interpolation of all the displacement parameters defined at each nodal point on the composite plate. Comparing with various existing composite plate models, it is found that simple C0 finite elements with non-zero normal strain could produce accurate deformations and stresses of thick multilayer composite plates subjected to thermal and mechanical loads.

The visual pullout model box was built, and a series of geogrid pullout tests were conducted to study the micro-macro feature of the soil/geogrid interface. Associating with image visual tracing technique and non-target measuring technique, displacement and shear strain field in the process of pullout was obtained. The results show that the apparent friction coefficient was related with the vertical stress, the sand particles show high gradient changes of displacement and concentration of shear strain in the interface region; the thickness of standard soil/geogrid interface is 6.5 times the average particle size. The study results contribute to providing a new understanding for more in-depth study on the mechanism of the reinforcement interface.

An assessment of a non-polynomial based higher order shear and normal deformation theory for vibration response of gradient plates with initial geometric imperfections

A hierarchical multiple plate models theory for laminated composites including delamination and geometrical nonlinear effects

Thermo-mechanics of undamaged and damaged multilayered composite plates: a sub-laminates finite element approach

On the effects of coupling between in-plane and out-of-plane vibrating modes of smart functionally graded circular/annular plates

SummaryShear locking is a major issue emerging in the computational formulation of beam and plate finite elements of minimal number of degrees of freedom as it leads to artificial overstiffening. In this paper, discontinuous Timoshenko beam and Mindlin‐Reissner plate elements are developed by adopting the Hellinger‐Reissner functional with the displacements and through‐thickness shear strains as degrees of freedom. Heterogeneous beams and plates with weak discontinuity are considered, and the mixed formulation has been combined with the extended finite element method (FEM); thus, mixed enrichment functions are used. Both the displacement and the shear strain fields are enriched as opposed to the traditional extended FEM where only the displacement functions are enriched. The enrichment type is restricted to extrinsic mesh‐based topological local enrichment. The results from the proposed formulation correlate well with analytical solution in the case of the beam and in the case of the Mindlin‐Reissner plate with those of a finite element package (ABAQUS) and classical FEM and show higher rates of convergence. In all cases, the proposed method captures strain discontinuity accurately. Thus, the proposed method provides an accurate and a computationally more efficient way for the formulation of beam and plate finite elements of minimal number of degrees of freedom.

The quintic finite element and finite strip with generalized degrees of freedom in structural analysis

The cone penetration test and the standard penetration test are perhaps the most versatile techniques for investigating soil properties in-situ. Advancing the probe through the soil requires substantial downforce due to friction between the probe and the soil. Inspired by the ability of worms to conform their body to the most mechanically advantageous shape while tunneling, an innovative self-excavating geo-probe has been developed and deployed in a laboratory environment. Analogous to a worm’s ability to expand its body, a soft balloon mounted behind a rigid cone is inflated or deflated by applying pressure or vacuum periodically to alter the cone penetration resistance. Laboratory experiments have shown promising results that the new geo-probe can penetrate the soil more efficiently. However, the interactions at balloon–soil–cone interfaces are complex and not fully understood. This numerical study focuses on the behavior of the geo-probe during balloon inflation and deflation. A two-dimensional discrete element model is developed to provide particle-level insight into the micromechanics of the interactions between the geo-probe and the soil. A baseline simulation is first conducted to study the failure mechanisms of the bulk soil during inflation and deflation. Additionally, the contact forces at balloon–soil and soil–cone interfaces are analyzed to show the variation of penetration resistance. The displacement field, shear strain field, and contact force chains are numerically investigated to gain a fundamental understanding of the tool–soil interaction. Then, the effect of balloon locations and overburden stresses on the behavior of the probe are studied by performing sensitivity analyses. This study provides a numerical technique to study the tool–soil interactions that was inaccessible in laboratory test. Implementation of the simulation results enables extrapolation of bench-scale testing to a wider range of stresses and boundary conditions.

A postprocess method using a displacement field of higher-order shell theory

ABSTRACTA variable kinematic 1D finite element (FE) method is presented for 3D thermoelastic analysis of rotating disks with variable thickness. The principle of minimum potential energy is used to derive general governing equations of the disks subjected to body forces, surface forces, concentrated forces, and thermal loads. To solve the equations, the 1D Carrera unified formulation (CUF), which enables to go beyond the kinematic assumptions of classical beam theories, is employed. Based on the 1D CUF, the disk is considered as a beam, which can be discretized into a finite number of 1D elements along its axis. The displacement field over the beam’s cross section is approximated by Lagrange expansions. This methodology leads to an FE formulation that is invariant with respect to the order of expansions used over the cross sections, and thus the 3D problem reduces to a 1D problem. The effect of the cross section discretization on displacement and stress fields is investigated. Results obtained from this method are in good agreement with the reference analytical and finite difference solutions. The proposed innovative method can be very effective in the thermoelastic analysis of rotating disks.

Robust layerwise C0 finite element approach based on a variable separation method for the modeling of composite and sandwich plates

A size-dependent third-order shear deformable plate model incorporating strain gradient effects for mechanical analysis of functionally graded circular/annular microplates