A new front surface heat flux calibration method for a 1-D nonlinear thermal system with a time-varying back boundary condition

A mathematical method is presented for time-domain simulation of coupled heave, pitch, and roll motions of a planing hull. This method is introduced by using 2D+t theory and employs potential field related to hydrodynamic impact of an asymmetric wedge with roll speed to solve four relations for the involved added masses in the motion. Momentum variation of the derived added mass terms is used to compute 2D normal force and roll moment. Two-dimensional hydrostatic moment and moment due to hydrodynamic forces are taken into consideration and time derivative of the wetted half-beam is determined by using the roll speed. Three-dimensional forces are computed by integrating the 2D forces over the length of the boat and new added mass terms are derived for the coupled heave, pitch, and roll motions. Ultimately, a nonlinear system of equations for the motion is presented by putting the forces together. Validity of the proposed method is assessed using an extensive set of test cases, which are conducted in four steps. Predicting coupled heave and pitch motions without roll motion, dynamic response of a 2D wedge due to asymmetric impact, computing the hydrodynamic coefficients in coupled heave and roll motions, and predicting roll motion of a planing boat due to a forced pitch motion are involved in the validation steps, respectively. Results of the first three steps are compared against experimental results, while the results of the last step are compared against the results of previously published simulations. Favorable agreement has been displayed between the obtained results and the available data in all of these steps. Finally, the proposed method is used to investigate the effects of the roll motion on the heave and pitch motions of planing hulls. Based on the obtained results, amplitudes of the heave and pitch motions exhibit an increase when the boat is free of roll which is due to an increase in the exciting force, accelerations, and reduction of heave and pitch added masses in this situation.     

An appropriate FE model for through-thickness variation of displacement and potential in thin/moderately thick smart laminates

A finite element model for the analysis of fibre-reinforced laminated composite plates embedded and/or surface bonded with piezoelectric layers and subjected to mechanical loading and/or electric potential has been presented in this paper. The proposed model is applicable for the analysis of thin-to-moderately thick plates. No restriction has been imposed on the pattern of variation of the potential across the plate thickness so that the potential can have any value even within the core. As the plates considered here are not too thick, the structural deformation has been modelled by single layer theory where the effect of shear deformation has been taken into account following Mindlin's hypothesis. For the electric potential, layer-wise theory has been applied, as the through-thickness variation of electric potential does not follow any specific pattern. This is the first attempt wherein a combination of single layer theory and layer-wise approach has been used to solve the coupled problem of piezoelectricity in plate bending. Numerical examples have been carried out to study the performance of the proposed approach.     

Dynamics of rotating paramagnetic particles simulated by lattice Boltzmann and particle dynamics methods

Novel biochemical sensors consisting of rotating chains of microscale paramagnetic particles have been proposed that would enable convenient, sensitive analyte detection. Predicting the dynamics of these particles is required to optimise their design. The results of lattice Boltzmann (LB) and particle dynamics (PD) simulations are reported, where the LB approach provides a verified solution of the complete Navier-Stokes equations, including the hydrodynamic interactions among the particles. On the other hand, the simpler PD approach neglects hydrodynamic interactions, and does not compute the fluid motion. It is shown that macroscopic properties, like the number of aggregated particles, depend only on the drag force and not on the total hydrodynamic force, making PD simulations yield reasonably accurate predictions. Relatively good agreement between the LB and PD simulations, and qualitative agreement with experimental data, are found for the number of aggregated particles as a function of the Mason number. The drag force on a rotating cylinder is significantly different from that on particle chains calculated from both simulations, demonstrating the different dynamics between the two cases. For microscopic quantities like the detailed force distributions on each particle, the complete Navier-Stokes solution, here represented by the LB simulation, is required.     

Low-velocity impact-induced damage of continuous fiber-reinforced composite laminates. Part I. An FEM numerical model

A numerical model for simulating the process of low-velocity impact damage in composite laminates using the finite element method is presented in this paper, i.e. Part I of this two part series on the study of impact. In this model, the 9-node Lagrangian element of the Mindlin plate with consideration of large deformation analysis is employed. To analyze the transient response of the laminated plates, a modified Newmark time integration algorithm previously proposed by the authors is adopted here. We also proved that the impact process between a rigid ball and laminated plates is a stiff system, therefore a kind of A(α) stable method has been advocated here to solve the motion equation of the rigid ball. Furthermore, various types of damages including delamination, matrix cracking and fiber breakage, etc. and their mutual influences are modeled and investigated in detail. To overcome the difficulty of numerical oscillation or instability in the analysis of the dynamic contact problem between delaminated layers using the traditional penalty methods, we have employed dynamic spring constraints to simulate the contact effect, which are added to the numerical model by a kind of continuous penalty function. Moreover, an effective technique to calculate the strain energy release rate based on the Mindlin plate model is proposed, which can attain high precision. Finally, some techniques of adaptive analyses have been realized for improving the computational efficiency. Based on this model, a program has been developed for numerically simulating the damage process of cross-ply fiber-reinforced carbon/epoxy composite laminates under low-velocity impact load. In Part II, this numerical model will be verified by comparing with the experimental results. Also the impact damage will be investigated in detail using this numerical approach.     

Numerical simulations of impact behaviour of thin steel plates subjected to cylindrical,conical and hemispherical non-deformable projectiles

In this paper, a numerical study of normal perforation of thin steel plates impacted by different projectile shapes is reported. The numerical simulations of this problem have been performed using a finite element code, ABAQUS-Explicit with a fixed and an adaptive mesh for the plate. To define the thermoviscoplastic behaviour of the material constituting the plate, the Johnson–Cook model has been used. This homogeneous behaviour has been coupled with the Johnson–Cook fracture criterion to predict completely the perforation process. Three kinds of projectile shape (blunt, conical and hemispherical) have been simulated with a large range of impact velocities from 190 to 600 m/s. The analysis considers the influence of adiabatic shear bands, plastic work and the gradient of temperature generated in the plate. The numerical results predict correctly the behaviour projectile-plate in agreement with experimental data published by other authors.     

Hydroelastic analysis of plates and some approximations

The paper concerns the modelling of very large pontoon-type floating structures by thin beams and plates of shallow draft, excited by regular waves. It is shown how the classical theory of hydroelasticity, involving the concepts of added mass and damping associated with the structural responses, may be reconciled with more recent formulations. In the latter, coupled equations for displacement and total hydrodynamic pressure are solved directly, without the breakdown into diffraction and radiation problems. A numerical model is adopted based on a Galerkin approach, and the nature of the various components of hydrodynamic loading on a shallow draft beam is investigated. The approach is then extended to the case of thin plate in waves, where the hydrodynamic effects are fully three dimensional.     

A uniform asymptotic solution for nonlinear surface acoustic waves

A complete investigation of the coupled amplitude theory of nonlinear surface acoustic waves on an isotropic elastic solid, which avoids the limitations encountered in previous theories, is given here. A complete, uniformly valid solution in the interior of the medium is derived. Perspective drawings to study asymptotically the growth-decay cycles the displacement and the velocity profiles, have also been done.     

Simulation of perforation and penetration in metal matrix composite materials using coupled viscoplastic damage model

In the first part of the two companion papers, theoretical formulation of the multiscale micromechanical constitutive model that couples the anisotropic damage mechanism with the viscoplastic deformation is presented. In the second part of these companion papers the numerical simulation of the computational aspects of the theory are elaborated. The perforation and penetration problem of metal matrix composites (MMCs) due to high impact loading is simulated. In this sense, the computational aspects of the developed theory are elaborated here. First, the verification of the developed model is performed through its numerical implementation in order to test the model predictions of the material characteristic tests. This encompasses uniaxial monotonic loading and unloading under different strain rates, uniaxial cyclic loading, and uniaxial loading and relaxation. The verified material routine of the developed model is then implemented in the explicit finite element code ABAQUS via the user defined subroutine VUMAT at each integration point in order to analyze the projectile impact and penetration into laminated composite plates.     

Instability and fragmentation of expanding liquid systems

This analysis pursues the underlying physics governing the expansion, dispersal and breakup of a thin walled steel right circular cylinder filled with liquid after being impacted by a high velocity aluminum sphere. The impact generates a radially expanding coherent thin shell of liquid which stays together to at least a diameter 8 times that of the original cylinder. An instability criterion is proposed and developed based on the opposing forces of stabilizing inertial pressures and destabilizing viscous resistance. This criterion is compared to test data where possible in order to ascertain its ability to predict liquid breakup of the shell. The breakup theory developed here predicts the extensive expansion of the unthickened liquid prior to fragmentation as observed in the experiments. This result lends some credence to the underlying physics pursued here and its ability to predict the onset of liquid fragmentation.     

Free-surface flow of a fluid body with an inner circular cylinder in impulsive motion

An analytical theory and numerical computations are developed for the two-dimensional free-surface flow of an initially circular layer of inviscid fluid surrounding a rigid circular cylinder. The two cylinders are initially concentric. The fluid packet is released from rest and the flow suddenly starts forced by gravity and by the simultaneous impulsive motion of the inner body. A small-time expansion of the fully nonlinear free-surface problem is developed and a closed-form solution is found up to third order for an arbitrary radius of the rigid cylinder. For the gravitational flow around the body at rest, the solution is extended up to fourth order. Free-surface profiles and hydrodynamic forces on the cylinder are calculated and discussed against numerical solutions of the exact unsteady nonlinear problem. Some basic features, such as the formation of an almost uniform layer surrounding the upstream side of the body, are captured by the theory quite well and only later on in time significant quantitative differences appear. Similarly, the behaviour of hydrodynamic loads is rather well predicted during initial stages preceding larger fluctuations observed on a longer time-scale.     

基于Taylor实验及理论分析的泡沫铝动态冲击特性研究

泡沫铝是一种优异的结构材料,有着广泛的应用前景,研究其冲击动力学性能具有重要的理论意义及工程应用价值。Taylor冲击实验主要利用圆柱弹体撞击刚性墙来获取弹体材料的动态响应数据,是一种重要的动态实验手段,在实体金属领域较为成熟。由于泡沫铝自身的可压缩性,经典Taylor理论无法适用,在一定假设基础上基于实验数据建立了针对泡沫铝动态冲击响应的Taylor分析模型,并验证了模型的有效性。实验结果表明：Taylor冲击后,泡沫铝子弹变形段平均密度随撞击速度的增加而增加,且当撞击速度大于110m/s时,其增长趋于平缓;泡沫铝子弹剩余长度随撞击速度的增加而减小,且近似呈线性关系。     

Hydrodynamic and mechanical behavior of multi-particle confined between two parallel plates

A coupled Computational Fluid Dynamics-Discrete Element Method (CFD-DEM) approach is used to investigate the hydrodynamic and mechanical behavior of multi-particle, which settle and horizontally transport between two parallel plates. The particle-fluid interaction is two-way coupled, while inter-particle and particles-walls interactions are calculated based on the soft-sphere model. The Joint Roughness Coefficient (JRC) is used to represent the roughness of planar walls, and its effect on particle transport is quantitatively studied. When particles transport between two parallel smooth plates, the planar walls exert extra hydrodynamic retardation, which causes particle transport velocity to decrease with the decrease in the aperture between two plates. In contrast, when particles transport between two parallel rough plates, due to frequent interaction between particles, the mechanical interaction-induced retardation starts to work and further decreases particle transport velocity. Particle longitudinal migration is frequent because of inter-particle interaction, which hinders its transverse transport and even causes particle agglomeration in a duct during horizontal transport. In addition, the mechanical retardation is significantly dependent of particle transport regimes, and its effect gradually increases and changes to be dominant at high particle Reynold number regime.     

沿水平向运动的水中截断圆柱体辐射波浪问题的解析解答

根据线性势波理论,分析了水中截断圆柱体作水平简谐运动时结构周围的辐射波浪。利用分离变量法,分别得到了含有未知常数的三个流体子域速度势的简谐表达形式,并采用一个较为简单的匹配方法使其在流体子域的共同边界上满足压力和法向速度的连续条件。于是求解得到了速度势,进而可得到由等效附加质量和附加阻尼表示的柱体侧面上的动水力。不仅能考虑自由表面波对动水压力的影响,也适用于位于任意水深处的截断圆柱体。实例分析表明,该方法具有较高的计算精度;同时对于截断圆柱体,采用Morison方程中的动水附加惯性力项会高估柱体侧面上的动水力。     

Buckling Analysis of Angle-ply Composite and Sandwich Plates by Combination of Geometric Stiffness Matrix

Buckling response of angle-ply laminated composite and sandwich plates are analyzed using the global-local higher order theory with combination of geometric stiffness matrix in this paper. This global-local theory completely fulfills the free surface conditions and the displacement and stress continuity conditions at interfaces. Moreover, the number of unknowns in this theory is independent of the number of layers in the laminate. Based on this global-local theory, a three-noded triangular element satisfying C¹ continuity conditions has also been proposed. The bending part of this element is constructed from the concept of DKT element. In order to improve the accuracy of the analysis, a method of modified geometric stiffness matrix has been introduced. Numerical results show that the present theory not only computes accurately the buckling response of general laminated composite plates but also predicts the critical buckling loads of soft-core sandwiches. However, the global higher-order theories as well as first order theories might encounter some difficulties and overestimate the critical buckling loads for soft-core sandwich plates.     

Hydroelastic behaviour of compound floating plate in waves

The paper deals with the plane problem of the hydroelastic behaviour of floating plates under the influence of periodic surface water waves. Analysis of this problem is based on hydroelasticity, in which the coupled hydrodynamics and structural dynamics problems are solved simultaneously. The plate is modeled by an Euler beam. The method of numerical solution of the floating-beam problem is based on expansions of the hydrodynamic pressure and the beam deflection with respect to different basic functions. This makes it possible to simplify the treatment of the hydrodynamic part of the problem and at the same time to satisfy accurately the beam boundary conditions. Two approaches aimed to reduce the beam vibrations are described. In the first approach, an auxiliary floating plate is added to the main structure. The size of the auxiliary plate and its elastic characteristics can be chosen in such a way that deflections of the main structure for a given frequency of incident wave are reduced. Within the second approach the floating beam is connected to the sea bottom with a spring, the rigidity of which can be selected in such a way that deflections in the main part of the floating beam are very small. The effect of the vibration reduction is quite pronounced and can be utilized at the design stage.     

Refined global–local higher-order theory for angle-ply laminated plates under thermo-mechanical loads and finite element model

To analyze angle-ply laminated composite and sandwich plates coupled bending and extension under thermo-mechanical loading, a refined global–local higher-order theory considering transverse normal strain is presented in this work. Hitherto, present theory for angle-ply laminates has never been reported in the literature, and this theory can satisfy continuity of transverse shear stresses at interfaces. In addition, the number of unknowns in present model is independent of layer numbers of the laminate. Based on this theory as well as methodology of the refined triangular discrete Kirchhoff plate element, a triangular laminated plate element satisfying the requirement of C¹ continuity is presented. Numerical results show that the present refined theory can accurately analyze the bending problems of angle-ply composite and sandwich plates as well as thermal expansion problem of cross-ply plates, and the present refined theory is obviously superior to the existing global–local higher-order theory proposed by Li and Liu [Li XY, Liu D. Generalized laminate theories based on double superposition hypothesis. Int J Numer Meth Eng 1997;40:1197–212]. After ascertaining the accuracy of present model, the distributions of displacements and stresses for angle-ply laminated plates under temperature loads are also given in present work. These results can serve as a reference for future investigations.     

Plastic deformation of polyurea coated composite aluminium plates subjected to low velocity impact

The demand for protective measures for structures is on the rise due to the increasing possibility of structural damage due to threats such as natural disasters, collision of vehicles, and blast and ballistic impacts. Application of an elastomer as a composite material with other base materials such as aluminium, steel and concrete has been considered as one of the measures to mitigate such threats. However, very limited work has been conducted in this area, especially on the feasibility of polyurea (elastomer) as a composite material against low velocity impacts. The focus of this research is to investigate the behaviour of polyurea coated composite aluminium plates subjected to rigid blunt-nosed projectile impact. AA5083-H116 aluminium alloy plates with polyurea coatings of 6 mm and 12 mm thickness were investigated. A blunt cylindrical projectile of high strength steel travelling in the velocity range of 5–15 m/s impacted at the centre of the 300 mm × 300 mm square plates. A polyurea coating was used to absorb part of the impact energy and provide protection to the plates as an energy damping material through application on the impact side of the plates. In addition, uncoated aluminium plates of the same thickness were used in the test program. A gas gun mechanism was used to fire a 5 kg projectile, and laser displacement monitoring equipment was used to record the out-of-plane deformation history of the plate during the impact. The complete test setup has been modelled numerically using the advanced finite element (FE) code LS-DYNA. The models were validated with the experimental results. Deformation time histories obtained from both the experimental and numerical studies for the plates were used to compare the ability of polyurea to effectively mitigate the damage resulting from low velocity impact. The polyurea coated plates showed a considerable reduction in out-of-plane deformation when compared to the uncoated plates. These findings indicate that polyurea can be utilised as an efficient energy absorbing/damping material against low velocity impact damage.     

Mathematical modeling of sway, roll and yaw motions: order-wise analysis to determine coupled characteristics and numerical simulation for restoring moment’s sensitivity analysis

This paper investigates sway, roll and yaw motions of a floating body with the aim to determine coupled motion characteristics based on the order-wise analysis of hydrodynamic coefficients. To compute the hydrodynamic coefficients and wave force exerted on the floating body, we employ speed-dependent strip theory. The governing equations are solved analytically for linear restoring moment. For nonlinear restoring moment which is expressed as an odd-order polynomial of fifth degree in roll angle, we apply the Runge–Kutta–Gill method to solve the coupled equations. To investigate the effect of initial disturbances on sway, roll, yaw and speed of the body, numerical experiments have been carried out for a Panamax Container ship under the action of a sinusoidal wave of periodicity 11.2 s with varying wave height and speed. For the linear restoring moment, we first derive associated motion equations for various cases based on the relative magnitude of the hydrodynamic coefficients. The order-wise analysis leads to the classification of coupled characteristics exhibiting the nature of coupling. For the nonlinear restoring moment, we notice that the initial disturbance plays an important role in the ship’s stability. The effects of forward speed and variation in wave heights are illustrated through typical numerical experiments.     

On the hydrodynamic approximation for long-rod penetration

Steady-state hydrodynamic theory, or variations thereof, has been applied to long-rod penetration since the 1940s. It is generally believed that projectile strength is of little consequence at high velocities, and that hydrodynamic theory is applicable to long-rod penetration when penetration pressures are much greater than the target flow stress. Substantiating this belief is the observation that at approximately 2.5 km/s, for tungsten alloy projectiles into armor steel, normalized penetration (P/L) nominally saturates to the classical hydrodynamic limit of the square root of the ratio of the projectile to target densities. Experimental data herein, however, show penetration velocities and instantaneous penetration efficiencies fall below that expected from hydrodynamic theory, even at impact velocities as high as 4.0 km/s. Numerical simulations, using appropriate strength values, are in excellent agreement with the experimental data. Parametric studies demonstrate that both projectile and target strength have a measurable effect even at such high impact velocities.     

A novel method for launching flyer plates

We describe a potential method for launching flat flyer plates by using explosives in complete cylindrical convergence. The basic problem we study in this computational analysis is how to turn the cylindrically convergent shock wave from the explosive into a flat front shock wave running parallel to the cylinder axis. We use a two-dimensional Lagrangian finite difference code to simulate the device. The code uses a free Lagrange method for dealing with mesh distortions.

The calculations predict that the method could launch relatively flat metal plates at velocities up to 14 km/s, but computational uncertainties make experimental verification mandatory.