NUMERICAL INVESTIGATION OF TOROIDAL SHOCK WAVES FOCUSING USING DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD

A numerical simulation of the toroidal shock wave focusing in a co-axial cylindrical shock tube is inves- tigated by using discontinuous Galerkin （DG） finite element method to solve the axisymmetric Euler equations. For validating the numerical method, the shock-tube problem with exact solution is computed, and the computed results agree well with the exact cases. Then, several cases with higher incident Mach numbers varying from 2.0 to 5.0 are simulated. Simulation results show that complicated flow-field structures of toroidal shock wave diffraction, reflection, and focusing in a co-axial cylindrical shock tube can be obtained at different incident Mach numbers and the numerical solutions appear steep gradients near the focusing point, which illustrates the DG method has higher accuracy and better resolution near the discontinuous point. Moreover, the focusing peak pres- sure with different grid scales is compared.

Enhanced wave and finite element method for wave propagation and forced response prediction in periodic piezoelectric structures

As a promising numerical tool of structural dynamics in mid- and high frequencies, the wave and finite element method（WFEM） is receiving increasingly attention and applications. In this paper, an enhanced WFEM has been developed with a reduced model and a new eigenvalue scheme. The reduced model is applicable for structures with piezoelectric shunts or local dampers;the new eigenvalue scheme can mitigate the ill-conditioning when the wave basis is calculated. The enhanced WFEM is applied to a thin-wall structure with periodically distributed piezoelectric materials（PZT）. Both free wave characteristics and forced response are analyzed and the influences of the suggested enhancements are presented. It is shown that if the control factors are properly chosen, these enhancements can improve the accuracy while accelerating the calculation. Resulting from the complexity of the application, these enhancements are not optional but imperative.

Wave propagation of laminated composite plates via GPU-based wavelet finite element method

This paper presents a novel parallel implementation technology for wave-based structural health monitoring (SHM) in laminated composite plates. The wavelet-based B-spline wavelet on he interval (BSWI) element is constructed according to Hamilton’s principle, and the element by element algorithm is parallelly executed on graphics processing unit (GPU) using compute unified device architecture (CUDA) to get the responses in full wave field accurately. By means of the Fourier spectral analysis method,the Mindlin plate theory is selected for wave modeling of laminated composite plates while the Kirchhoff plate theory predicts unreasonably phase and group velocities. Numerical examples involving wave propagation in laminated composite plates without and with crack are performed and discussed in detail. The parallel implementation on GPU is accelerated 146 times comparing with the same wave motion problem executed on central processing unit (CPU). The validity and accuracy of the proposed parallel implementation are also demonstrated by comparing with conventional finite element method (FEM) and the computation time has been reduced from hours to minutes. The damage size and location have been successfully determined according to wave propagation results based on delay-and-sum (DAS). The results show that the proposed parallel implementation of wavelet finite element method (WFEM) is very appropriate and efficient for wave-based SHM in laminated composite plates.

Numerical Simulation of the Solitary Wave Interacting with an Elastic Structure Using MPS-FEM Coupled Method

Fluid-Structure Interaction(FSI) caused by fluid impacting onto a flexible structure commonly occurs in naval architecture and ocean engineering. Research on the problem of wave-structure interaction is important to ensure the safety of offshore structures. This paper presents the Moving Particle Semi-implicit and Finite Element Coupled Method(MPS-FEM) to simulate FSI problems. The Moving Particle Semi-implicit(MPS) method is used to calculate the fluid domain, while the Finite Element Method(FEM) is used to address the structure domain. The scheme for the coupling of MPS and FEM is introduced first. Then, numerical validation and convergent study are performed to verify the accuracy of the solver for solitary wave generation and FSI problems. The interaction between the solitary wave and an elastic structure is investigated by using the MPS-FEM coupled method.

Finite Element Numerical Method for Nonlinear Interaction Response Analysis of Offshore Jacket Affected by Environment Marine Forces

In this paper a nonlinear response of a fixed offshore platform under the combined forces of waves, wind and sea currents is presented. Wave force acting on the elements is calculated using Morison equation. Hydrodynamic loads on horizontal and vertical tubular members and the dynamic response of offshore fixed platform coupled with distribution of displacement, axial force, and bending moment along the base of the platform for regular and severe cases have been investigated. The structure must be able maintain production in a one-year wave return period condition and also to be able to continue with one hundred-year storm return period. The results of this study show that bending moment values with a one-year wave return period condition for the base platform and junction of platform to deck are 70 percent and 59 percent, respectively more than bending moment with a one-year wave return period. The direction of wave and wind hit has significant effects on the shift platform response, also nonlinear response is important for the safe design and operation of offshore structures.

On the Total Dynamic Response of Soil-Structure Interaction System in Time Domain Using Elastodynamic Infinite Elements with Scaling Modified Bessel Shape Functions

This paper is devoted to a new approach—the dynamic response of Soil-Structure System (SSS), the far field of which is discretized by decay or mapped elastodynamic infinite elements, based on scaling modified Bessel shape functions are to be calculated. These elements are appropriate for Soil-Structure Interaction problems, solved in time or frequency domain and can be treated as a new form of the recently proposed elastodynamic infinite elements with united shape functions (EIEUSF) infinite elements. Here the time domain form of the equations of motion is demonstrated and used in the numerical example. In the paper only the formulation of 2D horizontal type infinite elements (HIE) is used, but by similar techniques 2D vertical (VIE) and 2D corner (CIE) infinite elements can also be added. Continuity along the artificial boundary (the line between finite and infinite elements) is discussed as well and the application of the proposed elastodynamical infinite elements in the Finite element method is explained in brief. A numerical example shows the computational efficiency and accuracy of the proposed infinite elements, based on scaling Bessel shape functions.

THE MUTUAL VARIATIONAL PRINCIPLE OF FREE WAVE PROPAGATION IN PERIODIC STRUCTURES

By taking infinite periodic beams as examples,the mutual variational principle for analyzing the free wave propagation in periodic structures is established and demonstrated through the use of the propaga- tion constant in the present paper,and the corresponding hierarchical finite element formulation is then de- rived.Thus,it provides the numerical analysis of that problem with a firm theoretical basis of variational prin- ciples,with which one may conveniently illustrate the mathematical and physical mechanisms of the wave prop- agation in periodic structures and the relationship with the natural vibration.The solution is discussed and ex- amples are given.

Numerical simulation of shock wave phenomena in hydrodynamic model of semiconductor devices

We propose a finite element method to investigate the phenomena of shock wave and to simulate the hydrodynamic model in semiconductor devices. An introduction of this model is discussed first. Then some scaling factors and a relationship between the changing variables are discussed. And then, we use a finite element method （P1-iso-P2 element） to discrete the equations. Some boundary conditions are also discussed. Finally, a sub-micron n%＋-n-n^＋ silicon diode and Si MESFET device are simulated and the results are analyzed. Numerical results show that electronic fluids are transonic under some conditions.

Fluid structure interaction for circulation valve of hydraulic shock absorber

Based on the working principle and the damping characteristic of hydraulic shock absorber, a fluid structure interaction method was presented, which was used to analyze the microcosmic and high-frequency processing mechanism of fluid structure interaction between circulation valve and liquid of hydraulic shock absorber. The fluid mesh distortion was controlled by the CEL language, and the fluid struc^tre interaction mathematical model was established. The finite element model was established by ANSYS CFX software and was analyzed by dynamic mesh technique. The local sensitive computational area was meshed by prismatic grid, which could reduce the negative volume problem during the simulation. The circulation valve and liquid of hydraulic shock absorber were simulated and analyzed under the condition of sinusoidal inlet velocity loads. Flow characteristic and dynamics characteristic were obtained. The pressure distribution and the displacement of circulation value were obtained, and the acceleration curve of circulation valve was simulated and analyzed. The conformity of the final simulation results with the experimental datum indicates that this method is accurate and reliable to analyze the dynamics characteristic between circulation valve and liquid of hydraulic shock absorber, which can provide a theoretical foundation for optimizing hydraulic shock absorber in the future.

Tensile Shock Physics in Compressible Thermoviscoelastic Solid Medium

This paper addresses tensile shock physics in thermoviscoelastic (TVE) solids without memory. The mathematical model is derived using conservation and balance laws (CBL) of classical continuum mechanics (CCM), incorporating the contravariant second Piola-Kirchhoff stress tensor, the covariant Green’s strain tensor, and its rates up to order n. This mathematical model permits the study of finite deformation and finite strain compressible deformation physics with an ordered rate dissipation mechanism. Constitutive theories are derived using conjugate pairs in entropy inequality and the representation theorem. The resulting mathematical model is both thermodynamically and mathematically consistent and has closure. The solution of the initial value problems (IVPs) describing evolutions is obtained using a variationally consistent space-time coupled finite element method, derived using space-time residual functional in which the local approximations are in hpk higher-order scalar product spaces. This permits accurate description problem physics over the discretization and also permits precise a posteriori computation of the space-time residual functional, an accurate measure of the accuracy of the computed solution. Model problem studies are presented to demonstrate tensile shock formation, propagation, reflection, and interaction. A unique feature of this research is that tensile shocks can only exist in solid matter, as their existence requires a medium to be elastic (presence of strain), which is only possible in a solid medium. In tensile shock physics, a decrease in the density of the medium caused by tensile waves leads to shock formation ahead of the wave. In contrast, in compressive shocks, an increase in density and the corresponding compressive waves result in the formation of compression shocks behind of the wave. Although these are two similar phenomena, they are inherently different in nature. To our knowledge, this work has not been reported in the published literature.

Short-Crested Waves Interaction with A Concentric Porous Cylinder System with Partially Porous Outer Cylinder

In this paper, based on the linear wave theory, the interaction of short-crested waves with a concentric dual cylindrical system with a partially porous outer cylinder is studied by using the scaled boundary finite element method （SBFEM）, which is a novel semi-analytical method with the advantages of combining the finite element method （FEM） with the boundary element method （BEM）. The whole solution domain is divided into one unbounded sub-domain and one bounded sub-domain by the exterior cylinder. By weakening the governing differential equation in the circumferential direction, the SBFEM equations for both domains can be solved analytically in the radial direction. Only the boundary on the circumference of the exterior porous cylinder is discretized with curved surface finite elements. Meanwhile, by introducing a variable porous-effect parameter G, non-homogeneous materials caused by the complex configuration of the exterior cylinder are modeled without additional efforts. Comparisons clearly demonstrate the excellent accuracy and computational efficiency associated with the present SBFEM. The effects of the wide range wave parameters and the structure configuration are examined. This parametric study will help determine the various hydrodynamic effects of the concentric porous cylindrical structure.

Application of the Hierarchical Functions Expansion Method for the Solution of the Two Dimensional Navier-Stokes Equations for Compressible Fluids in High Velocity

This work presents a new application for the Hierarchical Function Expansion Method for the solution of the Navier-Stokes equations for compressible fluids in two dimensions and in high velocity. This method is based on the finite elements method using the Petrov-Galerkin formulation, know as SUPG (Streamline Upwind Petrov-Galerkin), applied with the expansion of the variables into hierarchical functions. To test and validate the numerical method proposed as well as the computational program developed simulations are performed for some cases whose theoretical solutions are known. These cases are the following: continuity test, stability and convergence test, temperature step problem, and several oblique shocks. The objective of the last cases is basically to verify the capture of the shock wave by the method developed. The results obtained in the simulations with the proposed method were good both qualitatively and quantitatively when compared with the theoretical solutions. This allows concluding that the objectives of this work are reached.

Investigation of dynamics of discrete framed structures by a numerical wave-based method and an analytical homogenization approach

In this article, the analytical homogenization method of periodic discrete media（HPDM）and the numerical condensed wave finite element method（CWFEM） are employed to study the longitudinal and transverse vibrations of framed structures. The valid frequency range of the HPDM is re-evaluated using the wave propagation feature identified by the CWFEM. The relative error of the wavenumber by the HPDM compared to that by the CWFEM is illustrated in functions of frequency and scale ratio. A parametric study on the thickness of the structure is carried out where the dispersion relation and the relative error are given for three different thicknesses. The dynamics of a finite structure such as natural frequency and forced response are also investigated using the HPDM and the CWFEM.

应力波在有地下复合结构的岩石介质中传播规律研究

复合结构在抗动荷载方面具有明显的优势,它比一般的结构能够吸收更多的冲击能量。根据f 2.5 m爆炸模拟器上所做的实验结果和动力有限元方法对应力波的传播进行的计算,对应力波在有软回填层的地下复合圆形结构的介质中传播规律及与复合结构体系的相互作用进行了分析研究,给出了应力波在有软回填层的地下复合圆形结构的介质中传播规律。

梯度多胞牺牲层的抗爆炸分析

运用一维非线性塑性冲击波模型和细观有限元模型对密度梯度多胞牺牲层的抗爆炸性能进行了分析。基于率无关的刚性-塑性硬化模型,建立了描述冲击波在多胞牺牲层中传播的控制方程,分别给出了正、负密度梯度多胞材料在指数型爆炸载荷作用下的响应特性。研究了可正好吸收爆炸能量的梯度多胞牺牲层的临界厚度与载荷强度、覆盖层质量、多胞材料的密度梯度等参数之间的关系,给出了以临界厚度和支撑端应力峰值为指标的密度梯度设计图。运用二维细观有限元模型验证了基于非线性塑性冲击波模型的抗爆炸分析的有效性。

穿浪双体船横向强度与扭转强度的有限元计算

穿浪双体船的连接桥在横浪和斜浪中遭受比较大的横向弯矩和扭转力矩的作用,其自身的强度对穿浪双体船的安全性来说至关重要。本文在有限元理论的基础上,采用直接计算方法对一艘穿浪双体船进行了横向强度和扭转强度的整船有限元分析,对其总强度进行了校核,并初步分析了该船上层建筑对总横强度的影响。通过对计算结果的分析,掌握了该船的应力分布,为结构优化设计提供依据。

液压激波作用下管道流固耦合的动力学建模

为了研究在主动液压激波作用下管道振动的动力学特性,设计了一种液压激波变频控制系统,建立了激波作用下充液管道流固耦合的动力学模型.采用特征线-有限元法,用Newmark法编程,将由特征线法求得的流体各断面横向压力载荷施加到管道有限元的单元节点上,由此求得了管道横向各断面处及轴向的振动时程曲线,并通过快速傅里叶变换获取了管道横向及轴向的幅频特性曲线.试验发现,在激波作用下,充液管道的横向与轴向振动中基频的幅频特性吻合较好,而高阶频率由于谐波干扰信号非常严重,因此与数值模拟结果没有明确的对应关系.

集装箱船整船有限元结构分析

文章以一艘 1 70 0箱集装箱船为例 ,阐述了整船有限元结构分析方法。先建立全船有限元模型和质量模型 ,再用三维流体动力计算程序进行波浪随机载荷的长期预报 ,并在此基础上导出设计波参数组 ,最后 ,在全船有限元模型上计算得出船体结构在各个设计波上的应力分布和变形结果 ,所得到的船体结构有限元分析结果对同类型集装箱船的设计和强度分析有一定的参考价值 ,对其它类型的船舶结构强度分析也有一定的借鉴意义。

空中爆炸冲击波地面荷载的数值模拟

本文根据文献[1]的理论,给出地下防护结构动力有限元分析所需空中爆炸冲击波荷载的数值模拟方案,并编制出冲击波荷载自动生成程序,使地下防护结构有限元分析的效率与精度大大提高。

近地面TNT爆炸的试验研究和数值模拟

为了研究近地面化学爆炸的冲击波传播特性,在试验场进行了不同当量的TNT近地面爆炸试验,并应用有限元方法模拟了其中2种工况的冲击波传播过程。数值模拟结果与试验数据吻合较好,表明计算模型和参数选取的合理性和正确性,该模型和算法可以为进一步研究近地面爆炸冲击波传播特性提供有效手段。