闭合圆柱壳在冲击荷载下的动力计算

本文讨论闭合圆柱形壳体在冲击荷载作用下的动力计算.文中分析冲击过程各阶段的动量及能量的变化,并计入冲击物和被冲击的闭合圆柱壳系统质量的影响;用相当质量法将整个圆柱形壳体的分布质量转化为只有一个集中的“相当质量”,从而导出闭合圆柱形壳体在冲击力作用下的动力因数.本文的特点是具有实用价值,计算比较简便.     

闭合圆柱壳在轴向冲击荷载下的某些动力计算问题

本文讨论了闭合圆柱形壳体在轴向冲击荷载作用下的某些动力计算问题,其中包括动应力的计算和稳定性问题.文中分析了冲击过程中动量及能量的变化,并计入冲击物和被冲击的闭合圆柱壳系统质量的影响;用相当质量法将整个圆柱形壳体的分布质量转化为只集中在壳体一端的“相当质量”,从而导出闭合圆柱形壳体在轴向冲击荷载作用下的动力因数,因而解决了在上述受力情况下计算动应力的问题和求出临界荷重的问题.     

三维浮式结构的流固耦合动力特性分析

对于采用位移-压力有限元格式从流固耦合系统导出的大型非对称矩阵特征值问题,构造出了一种新格式的迭代Arnoldi方法进行非对称特征值分析来获得浮式结构的动力特性．该迭代格式在克服零频的移频技术中,可以高效地计算出Arnoldi向量．实例分析结果表明,流固耦合作用对水上大型薄壁浮式结构动力特性具有重要影响．     

用统一分析梁与有限节线法分析弹性薄壁截面构件

传统薄壁截面梁理论不仅与梁的长细比有关,还强烈地依赖于其横截面的形状和荷载的作用方式.为了解决任意长细比、任意形状弹性薄壁截面杆状类结构构件或结构体系受任意荷载作用的力学分析问题,提出了一种新的梁模型——统一分析梁,一种结构数值分析新方法——有限节线法.利用统一分析梁模型和有限节线法不仅可以分析任意弹性薄壁杆状类结构构件的力学行为,而且当问题的性质与传统梁理论的前提条件一致时,会得出同样精度的解答.算例计算结果证明了统一分析梁的合理性与有限节线法的正确性.     

地下结构变形速度在抗爆结构分析中的作用

在地下抗爆结构动力计算中,结构变形速度的作用是非常突出的.考虑结构变形速度的作用,所建立的结构体系运动微分方程可以真实地描述结构振动的实际情况.文中通过一维平面波理论,导出了作用在结构周边上的荷载表达式,给出了地下曲杆结构动力分析的广义变分原理,同时还进行了数值计算结构的对比分析.     

高层建筑结构空间静力、动力分析

本文采用JIGFEX程序系统,将高层建筑结构作为空间体系进行了较精确的空间静力、动力分析.对地震力和地震扭矩的计算提出了建议.为在中小型计算机上对大型复杂结构进行空间静力、动力分析提供了一个切实可行的计算途径.文内附有实际工程的计算结果和图表.     

爆炸和冲击载荷下金属材料及结构的动态失效仿真

通过数值模拟研究爆炸冲击载荷下金属材料和结构的动态失效规律对表征爆炸冲击毁伤效应及设计新型抗冲击结构具有重要意义.强动载下金属材料失效涉及材料大变形、热力耦合、材料状态变化等多个复杂物理过程,给数值仿真带来了极大挑战,其中包括裂纹、剪切带等复杂失效模式的几何描述、动态失效准则的确定、塑性与损伤耦合演化的描述等问题.针对这些挑战性问题,基于能量变分建立描述金属动态失效过程的热弹塑性相场理论和计算模型,实现了断裂与剪切带失效模式的统一描述,并提出了其显式有限元高效求解策略.进一步将该模型应用于爆炸冲击载荷下金属脆韧失效模式转变、绝热剪切带（ASBs）自组织及冲击波作用下薄壁圆盘失效形式转变三个典型金属动态失效问题,验证了理论模型的准确性及计算模型的稳健性.该工作为后续开展基于仿真的爆炸冲击毁伤评估及防护结构设计研究奠定了基础.     

无约束平面框架结构冲击响应分析(Ⅰ)——公式推导

运用广义Fourier级数方法推导了无约束平面框架结构受运动刚体冲击时的瞬态动力响应公式,利用这些公式得到冲击系统动力响应解析解．在公式推导过程中得出结构系统中弹性响应的动量之和为零的结论．从公式推导可以看出,模态分析法同样可以用来解决此类冲击问题．     

独柱式桥塔在冲击作用下的弹塑性时程分析

建立了独柱式桥塔结构的弹塑性动力学模型,并选择了脉冲荷载对结构进行加载计算。计算结果表明,桥塔结构受冲击作用后,层间残余位移的分布情况与冲击荷载作用位置有关。桥塔各部位的层间位移对冲击荷载的敏感性不同。相比塔的中部,塔的顶部和底部的层间位移对冲击荷载的敏感性更高。     

应力协调迭代法在高速冲击动力有限元中的应用

在EPIC[2][3],NONSAP[4]等弹塑性撞击动力有限元程序中,有一个共同的弱点是都采取了静力有限元方法,把位移函数用线性插值表示.单元之间应力是非协调的.因此应用虚功原理的基础不合理.为了克服以上困难,本文引入一个新的方法,即协调应力迭代法.实例表明,这种方法在冲击动力有限元计算中是稳定和精确的,同时具有减小单元刚度的作用.     

Topological design of multi-cell hexagonal tubes under axial and lateral loading cases using a modified particle swarm algorithm

Multi-cell structures have widely been studied due to their excellent energy absorption ability. However, few systematic studies have been conducted on the topological design of cross-sectional configurations of thin-walled tubes. To make full use of the material, topology optimization of multi-cell hexagonal tubes was conducted under both axial compression and lateral bending loadings. A binary particle swarm optimization (PSO) was enhanced by introducing the mass constraint factor to guide the movement of particles, which could improve the success rate of obtaining the global optimum. It was found that the optimum designs under the axial load placed the material outward to strengthen the interaction between the outer and inner walls and created more partitions between the inside rib walls. While under the lateral load, all the optimum designs have diagonally-connected elements to resist local deformation, and the material was also placed outward to increase the moment of inertia and thus to resist the global deformation. For the multiple loading cases, the final optimal designs are similar to the compression designs or combined designs from the two loading cases.     

Crashworthiness optimization of VRB thin-walled structures under manufacturing constraints by the eHCA-VRB algorithm

Variable-thickness rolled blanks (VRBs) represent an important approach for constructing lightweight structures. However, the optimization of the crashworthiness and thickness distribution of VRB thin-walled structures under manufacturing constraints is a nonlinear dynamic-response structural-optimization problem that has a large number of design variables. To tackle this problem, this paper has extended and improved the hybrid cellular automaton for thin-walled structures (HCATWS) algorithm, and has proposed an extended hybrid cellular automaton for VRB thin-walled structures (eHCA-VRB) algorithm. This algorithm consists of an outer loop and an inner loop. The outer loop performs crash simulation analysis to define an appropriate target mass for the inner loop, whereas the inner loop adjusts cell thicknesses according to the internal energy density (IED) of the current cell and its neighboring cells so that the IED in the design domain becomes evenly distributed. A one-dimensional CA model is defined along with the rolling direction based on the thickness distribution of VRB thin-walled structures. Furthermore, the eHCA-VRB algorithm also generates a mapping relationship between the one-dimensional CA model and the FE model. To optimize the thickness distribution of VRB thin-walled structures under manufacturing constraints, our method uses cell thickness as a design variable and incorporates the constraints of the VRB rolling process in the cell thickness update rules. To verify the convergence and efficiency of the eHCA-VRB algorithm, VRB top-hat thin-walled structures are optimized for crashworthiness with/or without manufacturing constraints (M.C.), respectively. The results show that the eHCA-VRB algorithm can be used to efficiently solve the optimization problems of crashworthiness and the thickness distribution of VRB thin-walled structures under manufacturing constraints.     

The geometrically nonlinear dynamic responses of simply supported beams under moving loads

This paper presents a method for determining the nonlinear dynamic responses of structures under moving loads. The load is considered as a four degrees-of-freedom system with linear suspensions and tires flexibility, and the structure is modeled as an Euler–Bernoulli beam with simply supported at both ends. The nonlinear dynamic interaction of the load–structure system is discussed, and Kelvin−Voigt material model is employed for the beam. The nonlinear partial differential equations of the dynamic interaction are derived by using the von Kármán nonlinear theory and D'Alembert's principle. Based on the Galerkin method, the partial differential equations of the system are transformed into nonlinear ordinary equations, which can be solved by using the Newmark method and Newton−Raphson iteration method. To validate the approach proposed in this paper, the comparison are performed using a moving mass and a moving oscillator as the excitation sources, and the investigations demonstrate good reliability.     

Simplification through regression analysis on the dynamic response of plates with arbitrary boundary conditions excited by moving inertia load

Dynamic response of a thin rectangular plate traversed by a moving inertia load with arbitrary boundary condition is investigated through this paper. The inertia effect of mass is considered and relevant formulation is established based on the full-term of acceleration, employing the method of Boundary Characteristic Orthogonal Polynomials, BCOP. To acquire the complete solution of partial differential equations governing on the plate, the Galerkin method is used to separate the temporal function from the spatial one. The problem is formulated in the state space and applying the numerical method of Matrix Exponential the complete solution would be achieved. In the numerical studies, a comprehensive parametric study is performed for both cases of loading when inertia effect is included or neglected. Several mass and aspect ratios for the plate with major types of boundary conditions CCCC, SSSS, CFCF and SFSF are accounted for presenting the results. Dynamic amplification factor against velocity parameter is scrutinized within many graphs alongside with a time history analysis of dynamic deflection for the plate's mid-span. Investigating on the dynamic response concludes to the critical boundary condition upon moving mass. By introducing a conversion factor, the margin of inertia and the critical velocity where happened would be achieved, then through a regression analysis a curve fitting model of polynomials is proposed. Corresponding coefficients testify the goodness of fit for such regression which are reported within tables. Referring to this simplified model of conversion factor pertaining to the specific boundary condition, it would be possible to handle the problem in moving load case without undertaking the complexities arisen from inertia contribution into the formulation. Having derived the factor from simplified model which has been calculated for a specific mass and velocity ratio, then multiplying into the moving load response, the complete solution for moving mass would be achieved.     

Size-dependent forced vibration of non-uniform bi-directional functionally graded beams embedded in variable elastic environment carrying a moving harmonic mass

In this study, general non-uniform material-varying micro-beam models under a moving harmonic load/mass are investigated. Material variation is modeled by combining axial and thickness material grading models using exponential, linear, parabolic and sigmoidal functions. Beam is assumed to be resting on an elastic foundation and in this linear foundation model, foundation modulus is assumed to vary axially with respect to space variable in a non-linear manner ignoring the effect of mass density of foundation on the behavior of micro-beam. Cross-section variation through the length is formulated for both thickness and width variation. Governing equations for such comprehensive beam model is achieved using Hamilton's principle in conjunction with modified couple stress theory to add the scale-effects and solved by discussing explicit and implicit finite element methods with using various-steps and Wilson-theta method. Current methodology is verified using previous studies on simplified problems. A comprehensive parametric study is presented in order to indicate the influence of each design, material and fundamental terms on the forced vibration behavior of such structures under a moving harmonic/constant load/mass. It is shown that by appropriately choosing the material variation in bidirectional functionally graded beams dynamic vibration behavior of such structures could change significantly. Moreover, it is shown that varying cross-section, elastic foundation and type of harmonic moving mass can change the dynamic reaction of the general micro-beam model. From the influence of modified couple stress term on mechanical behavior of such structures it is concluded that this term has crucial effect in varying the dynamic deflections and it is important to acknowledge it in analyzing such structures.     

A Four-node Finite Element for Piezoelectric Shell Structures in Convective Co-ordinates

In this contribution, an isoparametric piezoelectric shell element is presented which is based on convective coordinates and which allows for the analysis of arbitrary shell geometries. A two-field variation formulation [1, 2] is used in which the displacements and the electric potentials serve as independent variables. Especially, for thin-walled structures under certain boundary conditions and load cases, the displacement based element tend to shear and membrane locking. In order to avoid this poor behaviour, the Assumed Natural Strain (ANS) method [3] is introduced into the piezoelectric shell element. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic interaction of an elastic medium with a thin-walled curvilinear piezoelectric inclusion under longitudinal vibrations of a composite

Using the method of matched asymptotic expansions, we obtain models of dynamic interaction of a thin-walled curvilinear piezoelectric inclusion of variable thickness with an elastic isotropic matrix under stationary vibrations of the composite. The elastic system is under conditions of longitudinal shear. Different cases of electric boundary conditions on the surface of the heterogeneity are considered. We propose an algorithm for the construction of boundary layer corrections for refining the behavior of displacements and stresses in the vicinity of the edge of the inclusion for its different shapes.