Wide Range Of Plate Thicknesses Research Articles

A volume-averaged nodal projection method for the Reissner–Mindlin plate model

We introduce a novel meshfree Galerkin method for the solution of Reissner–Mindlin plate problems that is written in terms of the primitive variables only (i.e., rotations and transverse displacement) and is devoid of shear-locking. The proposed approach uses linear maximum-entropy basis functions for field variables approximation and is built variationally on a two-field potential energy functional wherein the shear strain, written in terms of the primitive variables, is computed via a volume-averaged nodal projection operator that is constructed from the Kirchhoff constraint of the three-field mixed weak form. The meshfree approximation is constructed over a set of scattered nodes that are obtained from an integration mesh of three-node triangles on which the meshfree stiffness matrix and nodal force vector are numerically integrated. The stability of the method is rendered by adding bubble-like enrichment to the rotation degrees of freedom. Some benchmark problems are presented to demonstrate the accuracy and performance of the proposed method for a wide range of plate thicknesses.

A hot-spot energy indicator for welded plate connections under cyclic axial loading and bending

Abstract The stress gradient near the weld toe caused by both the geometry and loading conditions can lead to significant scatters in the fatigue life of welded plate joints, driven by the same nominal or structural stress. This study proposes a volume-based hot-spot energy indicator near the weld toe to incorporate the stress gradients along both the surface and thickness directions for a wide range of plate thickness and different loading conditions. The comparison against reported experimental data validates the proposed volume-based hot-spot energy indicator, which reduces the scatter in the high-cycle fatigue lives of welded plate joints compared to the existing structural stress methods. To facilitate engineering applications, this study develops an analytical formulation to estimate the hot-spot energy indicator based on the notch stress intensity factors and Williams’ solution.

Fundamental study of CO2- and fiber laser cutting of steel plates with high speed visualization technique

Modified trim cut method with low level of invasion into the process is developed for visualization of laser cutting process. The method consists in high speed filming via transparent plate which slides with respect to the metal to allow visual access and simultaneously serves as the second missing wall of the kerf. The method is suitable for visualization in conditions equivalent to industrial cutting process in a wide range of plate thicknesses. High speed recordings are done for cutting of mild steel with oxygen and stainless steel with nitrogen. The effect of radiation wave length on the surface quality is studied by comparison of CO2 and fiber laser processing. The obtained results suggest that in case of oxygen assisted cutting, the combustion effects dominate on the surface quality and the effect of the radiation wavelength is moderate. In contrast, inert-gas-assisted cutting visualization reveals very high sensitivity to hydrodynamics of the melt flow which is strongly dependent on the radiation wavelength.

REISSNER-MINDLIN EXTENSIONS OF KIRCHHOFF ELEMENTS FOR PLATE BENDING

A method of extending various existing Kirchhoff elements to Reissner-Mindlin elements for plate bending is developed and tested. The essential idea is to use independent transverse shear strains and a special mixed formulation. The Nedelec edge element is effective for assuming the shear strains. Furthermore, the displacements are carefully constructed so that the strain-displacement relations are strictly satisfied for the transverse shear strains. We present our approach for displacement-based three-node triangular elements including both conforming and non-conforming ones as the base Kirchhoff elements. It is also possible to reduce the shear variables from the element degrees of freedom by means of a special technique called the beam element approximation. Numerical results are obtained for some fundamental test problems and are generally reasonable over wide range of plate thickness. In particular, it is observed that the tested elements actually reduce to the base Kirchhoff element in the thin plate range and are free from transverse shear locking.

Effect of additional exciton-polariton waves on the analytic properties of the optical response functions of thin crystal plates

The analytic properties of the complex amplitude reflection and transmission coefficients of plane-parallel crystal plates in the exciton spectral region in the presence of additional waves are considered in a wide range of plate thicknesses and angles of incidence of light. It is shown that violations of the classical amplitude-phase Kramers-Kronig relations for the reflection and transmission can be described quantitatively by the contributions of the reflection and transmission zeros appearing due to the interference of ordinary and additional exciton-polariton waves. The decrease in the total absorption coefficient in the vicinity of the exciton resonance is also explained by the presence of transmission zeros in the upper half-plane of the complex frequency.

On the Improvement of Calibration Coefficients for Hole-Drilling Integral Method: Part I—Analysis of Calibration Coefficients Obtained by a 3-D FEM Model

AbstractOne of the important factors affecting the accuracy of stress values obtained from the hole-drilling method is the calibration coefficient. A three-dimensional model was established to determine the calibration coefficients for integral method. The constraint conditions and loading conditions during hole-drilling can be simulated more realistically with this method. With this new model, coefficients a¯i,j and b¯i,j could be determined within one computation procedure. The relationship between calibration coefficients and plate thickness was investigated over a wide range of plate thickness. It has been found that the calibration coefficients determined in this work may vary with thickness of plates and the thickness range for thin plates was thus well defined. The calibration coefficients can thus be extended to measure the residual stresses of either thin or thick plates. Comparison of calibration coefficients with those determined by other studies was also conducted.

Fundamental solution and boundary element analysis of thick plates on Winkler foundation

This paper introduces for the first time a full derivation of a fundamental solution and boundary integral equations for thick Reissner plates resting on a Winkler elastic foundation, where the effect of transverse normal stresses resulting from the foundation reaction on the plate surface has been considered. The fundamental solution is derived by means of Fourier and Hankel integral transforms in terms of complex Bessel functions. Reduction of domain integral loading terms is provided for cases with uniformly distributed loadings, and concentrated shear forces. Case studies, with known analytical solutions, were analyzed using the developed theory, and it has been shown that the given formulations provide a very accurate solution for a wide range of plate thickness.

An efficient approach for boundary element bending analysis of thin and thick plates

This paper introduces a modified fundamental solution for bending analysis of thin and thick plates with arbitrary shapes. Kernel function terms representing the effect of transverse stresses have been separated, thus allowing efficient computation, within which such terms can be cancelled for thin plates. Boundary analysis of the domain loading terms for cases with uniform or linearly-distributed loading, and concentrated shear forces and bending moments are presented. A treatment of corner and singularity problems is also provided. Case studies with different shapes and boundary conditions, including a very thin example, have been analysed and the boundary element results were compared with corresponding analytical solutions. It is clear that the introduced derivations perform very well with a wide range of plate thickness.

Flux penetration and losses in steel plate with nonsinusoidal magnetisation

The cyclic magnetisation of steel plate with either nonsinusoidal magnetising force or nonsinusoidal voltage excitation is examined. The influence of the phase and the magnitude of the harmonic component of excitation is determined, together with profiles of flux density, voltage and magnetising force, at different depths and for a wide range of plate thicknesses and frequencies. A digital simulation technique, previously described, is used to compute theoretical values which include both hysteresis and eddy-current effects in the ferromagnetic material. Measured values of loss, flux/magnetising current loops and voltage waveshapes show good agreement with predicted values. A companion paper examines the cyclic magnetisation of non-grain-oriented low-loss steel laminations with nonsinusoidal excitation and computes theoretical values of loss, flux density and magnetising current waveshape.

A new type of plate bending element

Based on a two-field generalized variational principle, a new type of arbitrary quadrilateral plate bending element, with four nodes and with the effect of transverse shear deformation taken into account, is proposed. The element is applicable to a wide range of plate thickness and an explicit expression of stiffness matrix can be obtained. Therefore, it possesses the distinguished features of general applicability, high precision and less computer time.