Thick Plate Structures Research Articles

An SPH formulation for general plate and shell structures with finite deformation and large rotation

In this paper, we propose a reduced-dimensional smoothed particle hydrodynamics (SPH) formulation for quasi-static and dynamic analyses of plate and shell structures undergoing finite deformation and large rotation. By exploiting Uflyand–Mindlin plate theory, the present surface-particle formulation is able to resolve the thin structures by using only one layer of particles at the mid-surface. To resolve the geometric non-linearity and capture finite deformation and large rotation, two reduced-dimensional linear-reproducing correction matrices are introduced, and weighted non-singularity conversions between the rotation angle and pseudo normal are formulated. A new non-isotropic Kelvin-Voigt damping is proposed especially for the both thin and moderately thick plate and shell structures to increase the numerical stability. In addition, a shear-scaled momentum-conserving hourglass control algorithm with an adaptive limiter is introduced to suppress the mismatches between the particle position and pseudo normal and those estimated with the deformation gradient. A comprehensive set of test problems, for which the analytical or numerical results from literature or those of the volume-particle SPH model are available for quantitative and qualitative comparison, are examined to demonstrate the accuracy and stability of the present method.

Comparison of the Microstructural, Mechanical and Corrosion Resistance Properties of Ti6Al4V Samples Manufactured by LENS and Subjected to Various Heat Treatments.

In this paper, the influences of two post-heat treatments on the structural, mechanical and corrosion resistance properties of additively manufactured Ti6Al4V alloys were discussed in detail. The materials were produced using the laser engineering net shaping (LENS) technique, and they were subjected to annealing without pressure and hot isostatic pressing (HIP) under a pressure of 300 MPa for 30 min at temperatures of 950 °C and 1050 °C. Annealing without pressure led to the formation of a thin plate structure, which was accompanied by decreasing mechanical properties and increasing elongation and corrosion resistance values. For the HIP process, the formation of a thick plate structure could be observed, resulting in the material exhibiting optimal mechanical properties and unusually high elongation. The best mechanical and corrosion resistance properties were obtained for the material subjected to HIP at 950 °C.

Seismic resistance calculation in multi-story structures under vibration forces

The article is devoted to developing methods for solving the problem of seismic vibrations using a continuous spatial plate model of a multi-story building developed within the framework of the bi-moment theory of thick plate structures. A method for dynamic spatial calculations for seismic resistance of multi-story buildings under longitudinal seismic influences is proposed. Formulas are given for determining the reduced elastic moduli. The values of eigenfrequencies, displacements, and stresses are determined within the framework of the resonance method.

A refined quasi-3D isogeometric model for dynamic instability of graphene nanoplatelets-reinforced porous sandwich plates

This study pays attention to the dynamic instability behavior of advanced sandwich plate structures subjected to periodic in-plane compressive loads. By utilizing a powerful and efficient computational approach based on a four-variable refined quasi-3D plate theory and NURBS-based isogeometric analysis (IGA), the dynamic behavior of structures can be accurately evaluated while accounting adequately for the thickness stretching effect of normal deformation. To investigate the dynamic instability behavior, this study examines sandwich plate models that consist of two graphene nanoplatelets (GNPs)-reinforced skin layers and a porous core layer with two typical distributions of internal porosity: uniform and symmetric dispersion. Bolotin's method is applied in this study to solve the Mathieu–Hill equation and obtain the boundary of dynamic instability zones. Numerical examples are performed to examine the influence of various input parameters on the instability regions, as well as to provide new insights into the dynamic instability behavior of advanced sandwich plates under compressive loading which has not been comprehensively studied in the literature. The findings of this study suggest that the thickness stretching effect should be carefully evaluated for moderate to thick plate structures, such as sandwich plates.

Multi-Component Evaporation and Uneven Aluminum Distribution during High-Power Vacuum Laser Welding of Ti-6Al-4V Titanium Alloy

Titanium alloy is an important material for the manufacture of key components of deep-sea submersibles. High-power vacuum laser welding is an important method for welding TC4 thick plate (40–120 mm) structures. However, due to the low melting point of aluminum, its uneven distribution in the weld caused by evaporation during welding affects the quality of joints. This paper conducted experimental and simulation studies to investigate the effect of process parameters on multi-component evaporation and uneven aluminum distribution. Based on a three-dimensional model of vacuum laser welding, the mechanism of the uneven distribution of aluminum in the weld is explained. The results show that the uneven distribution of aluminum in the weld is mainly related to the metal vapor behavior and keyhole morphology. As the welding speed rises from 1 m/min to 3 m/min, the proportion of aluminum in the metal vapor and the degree of compositional unevenness increase. When the laser power increases from 6 kW to 18 kW, the proportion of aluminum in the metal vapor and degree of unevenness increase, peak at 12 kW, and then decrease. This work facilitates the selection of suitable process parameters to reduce aluminum evaporation during the high-power vacuum welding of Ti-6Al-4V alloys. Joints with a more stable performance can be obtained by avoiding the uneven distribution of aluminum.

Cause Analysis of Low Tensile Plasticity in Normal Direction for Hot‐Rolled Thick Plate of HSLA Steel

To investigate the cause for the low tensile plasticity in normal direction of high‐strength low‐alloy steel thick plate, tensile fracture observation, inclusion statistic, and microstructure observation of thick plate and solidification structure observation of continuous casting slab are carried out. The experimental results reveal that many MnS inclusions are only distributed on the platform of the tensile fracture and they only appear in the center of thick plate together with martensite and severe macrosegregation of elements C and Mn. It is concluded that the aggregated large‐sized MnS inclusions are the direct cause for reducing the tensile plasticity. Stress concentration on a single MnS inclusion during tensile testing can occur and cause a limited brittle fracture area. Aggregation of MnS inclusions creates a large brittle fracture area, which significantly reduces the tensile plasticity. The root cause of the aggregation of MnS inclusions is the well‐developed columnar crystals of continuous casting slab. The well‐developed columnar crystals push high concentration of solutes into the residual liquid‐phase zone in the center of continuous casting slab and create severe central macrosegregation which eventually lead to the appearance of aggregated large‐sized MnS inclusions with martensite in the center of thick plate.

Analytical Solution for the Static Bending Elastic Analysis of Thick Rectangular Plate Structures Using 3-D Plate Theory

In the current work, an analytical solution for static bending analysis of the thick rectangular plate structure was obtained using three-dimensional plate theory. First, the energy equation was formulated from the static elastic principles and transformed into a compatibility equation through general variation to get the slope and deflection relationship. The solution of the compatibility equation gave rise to the exact polynomial deflection function. In contrast, the coefficient of deflection and shear deformation of the plate was obtained from the governing equation through the direct variation method. These solutions were used to obtain the characteristic expression for analyzing the displacement and stresses of a rectangular plate. This formula was used for the solution of the bending problem of rectangular plate support conditions of two clamped edges, one free edge, and a simply-supported edge (CCFS). The result of the deflection and stresses decreases as the span-thickness ratio increases. More so, the aspect ratio effect of the shear stress of isotropic plates is investigated and discussed after a comparative analysis between the present work and previous studies. The result shows that the present study differs with RPT) of assumed deflection by 2.7%, whereas exact 2-D RPT by 1.9%. This shows the efficacy of the exact 3-D plate theory for rectangular plate analysis under CCFS support and loading condition.

Damage detection in thick plate structures based on ultrasonic SH wave

Thick plate structures are widely used in large deep-sea scientific detection equipment, such as deep-sea human-occupied vehicles, but they are prone to local damage caused by fatigue due to the complex working environment load. To prevent structural failure due to damage accumulation, it is necessary to carry out structural health monitoring for thick plate structures. In this work, two half-ring thickness poled d15 mode omnidirectional shear horizontal (SH) wave piezoelectric transducers are used to form an exciter/receiver network, and the SH2 mode wave packet is selected as the damage location wave packet. Then, the reconstruction algorithm for the probabilistic inspection of damage and an algorithm based on the time of guided wave flight are applied for damage detection in a 30 mm-thick aluminium plate. Experimental results show that structural damage detection based on SH waves can effectively identify and locate thick plate structural damage and evaluate the damage depth.

Effect of Residual Stress on Hydrogen Diffusion in Thick Butt-Welded High-Strength Steel Plates

Thick high-strength steel plates are increasingly being used for ship structures. Moreover, hydrogen enters the process of manufacturing and service, and large residual tensile stress occurs near the weld. Such stress can facilitate the diffusion and accumulation of hydrogen in the material, leading to hydrogen embrittlement fracture of the shell. Therefore, residual-stress-induced diffusion and accumulation of hydrogen in the stress concentration region of thick butt-welded high-strength steel plate structures need to be studied. In this study, manual metal arc welding was realized by numerical simulation of residual stress in a thick butt-welded high-strength steel plate model using the thermoelastic–plastic theory and a double ellipsoidal heat source model. To analyze residual stress, a set of numerical simulation methods was obtained through comparative analysis of the test results of relevant literature. Residual and hydrostatic stress distributions were determined based on these methods. Then, hydrogen diffusion parameters in each region of the model were obtained through experimental tests. Finally, the results of the residual stress field were used as the predefined field of hydrogen diffusion to conduct a numerical simulation analysis. The distribution of hydrogen diffusion under the influence of residual stress was obtained based on the theory of stress-induced hydrogen diffusion. The weak area of the welding joint was found to be near the weld toe, which exhibited high hydrostatic stress and hydrogen concentration. Further, the maximum hydrogen concentration value of the vertical weld path was approximately 6.1 ppm, and the maximum value of the path parallel to the weld centerline and 31 mm away from the weld centerline was approximately 6.22 ppm. Finally, the hydrostatic tensile stress in the vertical weld path was maximized (~345 MPa), degrading the material properties and causing hydrogen-related cracking. Hence, a reliable method for the analysis of hydrogen diffusion according to residual stress in thick high-strength steel plates was obtained. This work could provide a research basis for controlling and eliminating the adverse effects of hydrogen on the mechanical properties of ship structures and ensuring the safe service of marine equipment.

Welding distortion prediction and mitigation in thick steel plate structures on ships

ABSTRACT In the ship fabrication process, welding distortion will affect the dimension accuracy. In this paper, an industrialisation prediction method for thick steel plate structures on ships is proposed based on a combination of thermal-elastic-plastic finite element method and inherent deformation theory to reduce the welding distortion in the design stage, and its applicability is verified through a comparison of measurements in the shipyard and numerical simulations. The thick plate models produced by multi-pass welding technology are selected to analyse the welding distortion. The results show that the numerical prediction results are in good agreement with the measurement on site. The transverse bending distortion is the main factor that affects the fabrication accuracy. To mitigate welding distortion, the influence of welding sequence and flame heating is examined. This research may provide a macro concept for understanding the distribution characteristics of welding distortion and serve as a mitigation reference for manufacturing engineers.

Numerical study and experiments on the elasto-visco-plastic bifurcation buckling of thick anisotropic plates

The present work investigates the elasto-visco-plastic buckling of thick plate structures. Methods to estimate the buckling of thin elasto-visco-plastic shells and plates are proposed in literature. To the knowledge of the authors, only few works present experimental results, and none treat the experimental elasto-visco-plastic buckling of thick plate. Thick rectangular plates are chosen as a structure of interest to study elasto-visco-plastic buckling. A modelling/experimental approach is followed to solve such problem. Buckling experiments at room temperature on thick elasto-visco-plastic plates subjected to compressive load are performed. 3D digital image correlation (3D-DIC) is used to measure displacement fields on plate surface during buckling experiments. The experiments are also modelled through a finite element model. Bodner’s approach is coupled to Hencky’s deformation theory to predict buckling of elasto-visco-plastic plates. Bifurcation analysis are performed to estimate buckling critical stresses and strains, and buckling modes. Geometrical and loading imperfections are also discussed. A good correlation is observed between numerical results and experiments. The limitation of Bodner’s approach is also discussed.

Measurement of the Acoustic Non-Linearity Parameter of Materials by Exciting Reversed-Phase Rayleigh Waves in Opposite Directions.

The acoustic non-linearity parameter of Rayleigh waves can be used to detect various defects (such as dislocation and micro-cracks) on material surfaces of thick-plate structures; however, it is generally low and likely to be masked by noise. Moreover, conventional methods used with non-linear Rayleigh waves exhibit a low detection efficiency. To tackle these problems, a method of exciting reversed-phase Rayleigh waves in opposite directions is proposed to measure the acoustic non-linearity parameter of materials. For that, two angle beam wedge transducers were placed at the two ends of the upper surface of a specimen to excite two Rayleigh waves of opposite phases, while a normal transducer was installed in the middle of the upper surface to receive them. By taking specimens of 0Cr17Ni4Cu4Nb martensitic stainless steel subjected to fatigue damage as an example, a finite element simulation model was established to test the proposed method of measuring the acoustic non-linearity parameter. The simulation results show that the amplitude of fundamentals is significantly reduced due to offset, while that of second harmonics greatly increases due to superposition because of the opposite phases of the excited signals, and the acoustic non-linearity parameter thus increases. The experimental research on fatigue damage specimens was carried out using this method. The test result was consistent with the simulation result. Thus, the method of exciting reversed-phase Rayleigh waves in opposite directions can remarkably increase the acoustic non-linearity parameter. Additionally, synchronous excitation with double-angle beam wedge transducers can double the detection efficiency.

Weight Optimization of Thick Plate Structures Using Radial Basis Functions Parameterization

This study sought to optimize the weight of thick plate structures with topology optimization. Topology optimization is a numerical method for identification of voids in the design domain, to aid weight and material reduction. The level set approach is a new method in topology optimization. In this work, the radial basis functions level set approach is used to parameterize the continuum domain. The radial basis functions are used to parameterize the level set functions, which comprise axial symmetric, real value functions. These functions are suitable tools for function approximation. Thick plates are one of the most useful and familiar geometries in structural and mechanical engineering applications. Topology optimization of such structures would be very useful to identify efficient and lightweight plate structures. In this paper, the effectiveness of the parametric level set approach in topology optimization of clamped plate is demonstrated. The results show smooth boundaries and there are no intermediate densities, which constitutes a major advantage.

Tunnel boring machine cutterhead crack propagation life prediction with time integration method

Fatigue damage is one of the most common failure modes of large-scale engineering equipment, especially the full-face tunnel boring machine with characteristics of a thick plate structure bearing strong impact load. It is difficult to predict the location and propagation life of crack of cutterhead under strong impact load. Unseasonal maintenance of equipment caused by inaccurate prediction of life cycle of cutterhead seriously affects the construction efficiency of the equipment and the life safety of the operators. Determining the crack location of tunnel boring machine cutterhead structure under strong impact load and predicting the crack propagation life are difficult scientific problems. To solve them, first, the location of the stress concentration of the cutterhead is determined by using finite element analysis method of statics. Second, prediction model for crack propagation life of tunnel boring machine cutterhead characteristic substructure based on time integration is built. And the test of crack growth of cutterhead characteristic substructure is performed. The feasibility and accuracy of the prediction model are verified by contrasting crack prediction models and the results of the test. Finally, the life prediction of tunnel boring machine cutterhead of water diversion project in Northwest Liaoning Province is carried out by using crack propagation model based on time integration. Results show that the maximum error of theoretical prediction and experimental results of crack propagation is 16%. So the feasibility of crack propagation model based on time integration in predicting the crack growth of cutterhead is verified. It is predicted that the tunnel boring machine cutterhead panel can work normally for 5.9 km under the condition of ultimate load. Building the crack propagation model considering the influence of plate thickness and strong impact load has important research value for improving the working efficiency of engineering equipment, prolonging service time, and improving the working safety.

Single-pass arc welding of thick plate structures of 22K steel under a thin slag layer

The efficiency of single-pass automatic arc welding under a thin slag layer (ATL) with the forced formation of weld metal of welded joints in 22K steel with a thickness of 70 mm is shown. The optimum heat input in ATL welding makes it possible to produce in a single pass a welded joint with a finer structure and higher mechanical properties in comparison with electroslag welding. Recommendations for using the ATL method in welding production are outlined.

New benchmark solutions for free vibration of clamped rectangular thick plates and their variants

It is of significance to explore benchmark analytic free vibration solutions of rectangular thick plates without two parallel simply supported edges, because the classic analytic methods are usually invalid for the problems of this category. The main challenge is to find the solutions meeting both the governing higher order partial differential equations (PDEs) and boundary conditions of the plates, i.e., to analytically solve associated complex boundary value problems of PDEs. In this letter, we extend a novel symplectic superposition method to the free vibration problems of clamped rectangular thick plates, with the analytic frequency solutions obtained by a brief set of equations. It is found that the analytic solutions of clamped plates can simply reduce to their variants with any combinations of clamped and simply supported edges via an easy relaxation of boundary conditions. The new results yielded in this letter are not only useful for rapid design of thick plate structures but also provide reliable benchmarks for checking the validity of other new solution methods.

Analysis of anisotropic gradient elastic shear deformable plates

In this paper, Reddy’s third-order shear deformable plate theory is employed for the analysis of centrosymmetric anisotropic plate structures within strain gradient elasticity. The general three-dimensional anisotropic gradient theory is reduced to a two-dimensional formulation for the analysis of thick plate structures. The third-order shear deformation theory (TSDT) takes into account quadratic variation of the transverse shear strains of the plate and does not require shear correction factors. In order to investigate the case of small strains but moderate rotations, the von Karman strains are considered. The TSDT is also simplified to anisotropic Kirchhoff plate theory within gradient elasticity. To study specific material properties in more detail, the (Kirchhoff and TSDT) gradient plate theory of general anisotropy is simplified to the more practical case of orthotropic plates. It is observed that the gradient theory provides the capability to capture the size effects in anisotropic plate structures. As case studies, the bending and buckling behaviors of the simply supported orthotropic (Kirchhoff and TSDT) plates are studied. Variationally consistent boundary conditions are also discussed. Finally, analytical solutions are presented for the bending and buckling of simply supported orthotropic Kirchhoff plates. The effects of internal length scales on deflections and buckling loads are presented.

Residual Deflections and Stresses in a Thick T-Joint Plate Structure

In this paper transient thermo-elastic-plastic problem of a thick rectangular T-joint fillet weld plates is solved numerically in which we need to determine the temperature distribution, thermal deflections and stresses when the boundary conditions are known. At the T-joint section (weld pool area) high constant temperature is considered initially and convection boundary conditions are applied at other three edges as well as top and bottom surface of the plate. T-joint section and vertical plate is fixed (case 1) for plate stability, only T-joint section is fixed (case 2) as a boundary constraint for stress analysis. Numerical technique (Finite element method, Ansys software) is used to obtain the solution of the boundary value problem.

등기하 퇴화쉘 요소를 이용한 판과 쉘의 기하학적 비선형해석

In this study, geometrically nonlinear analysis of plate and shell structures is carried out by using a degenerated shell element. The present shell element is formulated by using the isogeometric concept. Reissner-Mindlin assumption is adopted in the element formulation where total Lagrange formulation is used. In particular, the positions of control points is consistently used to create the normal vector for the mapping between control points and associated points on real surface. The arc-length method is employed to handle the snap-through behaviour of shells. Several benchmark tests are tackled to verify the performance of the present shell element. From numerical tests, the present shell element can remove locking phenomena with the only use of refinement technique and it performs satisfactorily for both thin and thick plate and shell structures under geometrically nonlinear situations.

Experimental study on the through-thickness properties of structural steel thick plate and its heat-affected zone at low temperatures

Lamellar tearing and crack-induced brittle failures along steel plates in the through-thickness direction seriously threaten the safety and reliability of steel thick plate structures in construction and service, especially at low ambient temperatures. Three kinds of tests, including uniaxial tensile tests, Charpy V-Notch impact tests, and three-point bending (TPB) tests were performed at normal and low temperatures to investigate the through-thickness mechanical properties, impact and fracture toughness of Q345B structural steel plates with thicknesses from 60 to 165 mm. The test specimens were mainly sampled along the through-thickness direction of the plate, but transverse specimens along the rolling direction were also involved. The ductility index (percentage reduction of area), impact toughness index (Charpy impact energy), and fracture toughness index (critical crack tip opening displacement (CTOD) values) all decrease as the temperature declines. All the mechanical properties and the impact and fracture toughness along the through-thickness direction are worse than those along the rolling direction. The results also offer experimental support for the determination of an evaluation indicator for structural steel thick plates with through-thickness characteristics.