Nonlinear dynamic analysis of stiffened plates

A new finite strip formulation for the nonlinear analysis of stiffened plate structures subjected to transient pressure loadings is presented. The effects of large deflections, and strain rate sensitive yielding material properties are included. An explicit central difference/diagonal mass matrix time stepping method is adopted. Example results are presented for an I-beam, an isotropic plate and a five-bay stiffened panel and compared with other predictions and/or experimental results. It is observed that design level accuracy can be obtained for practical structures for a fraction of the cost of full finite element analyses.     

Nonlinear behavior of shells of revolution under cyclic loading

A large deflection elastic-plastic analysis is presented applicable to orthotropic axisymmetric plates and shells of revolution subjected to monotonie and cyclic loading conditions. The analysis is based on the finite-element method. It employs a new higher order, fully compatible, doubly curved orthotropic shell-of-revolution element using cubic Hermitian expansions for both meridional and normal displacements. Both perfectly plastic and strain hardening behavior are considered. Strain hardening is incorporated through use of the Prager-Ziegler kinematic hardening theory, which predicts an ideal Bauschinger effect. Numerous sample problems involving monotonie and cyclic loading conditions are analyzed. The monotonie results are compared with other theoretical solutions. Experimental verification of the accuracy of the analysis is also provided by comparison with results obtained from a series of tests for centrally monotonically-loaded circular plates that are simply supported at their edges.     

Simulation and experimental analysis of thermo-mechanical behavior of microresonators under dynamic loading

Simulation, finite element analysis and experimental investigations of the dynamical response of a microresonator under electrostatic actuation are presented in this paper. The scope of this paper is to characterize the influence of thermo-mechanical behavior of the material on the frequency response, amplitude and velocity of oscillations under continuous actuation. The effect of the thermoelastic damping on vibrating structures is experimentally investigated by measuring the loss in amplitude and velocity of oscillations as a function of time and the changes in quality factor. The tests are performed in ambient conditions and in vacuum in order to separate the extrinsic damping of beam by the intrinsic effect given by the thermoelastic damping. The vibrating structure under investigation is a polysilicon clamped–clamped beam.     

The dynamic behavior of fractal-like tubes with Sierpinski hierarchy under axial loading

To improve the energy absorption characteristics of regular triangular tubes, a novel thin-walled structure named as Sierpinski hierarchical triangular (SHT) tube is proposed by connecting the midpoint of each side of regular triangular tube. Finite-element (FE) model established by LSDYNA is developed to explore the mechanical behavior of SHT tube under axial loading, and the numerical models are validated by test results. Numerical simulations show that the dominant deformation mechanisms of SHT structure are in-extensional and extensional folding element. Based on Simplified Super Folding Element (SSFE) theory, mean crushing force of SHT tubes is deduced subsequently. The results show that the introduction of Sierpinski hierarchy significantly enhance energy absorption capacity. The mean crushing force of 1st, 2nd, and 3rd SHT tubes tend to increase by 70.5%, 113.2%, and 150.1% compared with the single-cell triangular (ST) tubes under the same relative density, respectively. Therefore, these studies encourage designers to introduce Sierpinski hierarchy in potential applications of thin-walled structures as energy absorption equipment.

     

Nonlinear transient response of stiffened plates to air blast loading by a superelement approach

In this paper, new plate and stiffener beam elements are developed for the nonlinear dynamic analysis of stiffened plate structures subject to blast-type pressure waves. The displacement fields for the elements are represented by polynomial and analytical functions in both in-plane directions and they have been constructed so that only one element per bay or span is required to model the response. Geometric and material nonlinearities are included and the temporal equations are solved by the implicit Newmark beta method with Newton-Raphson sub-iteration. The new formulation has been tested on several numerical examples and the results obtained are compared with other available solutions. The present model is simple, requires much reduced storage and computing time and yet gives results suitable for practical design purposes.     

Optimal design of rigid-plastic structures under dynamic loading

The optimal design of rigid-plastic beams with piecewise constant thickness under impulsive or dynamic pressure loading is considered. Such dimensions of the structure for which the beam of constant volume attains a minimum of local or mean residual deflection are sought. The equations of motion are integrated (i) exactly and (ii) approximately by making use of the method of mode form solutions. The method of solution is applied also to reinforced beams.The stiffness of the beam can be increased if we provide it with additional supports. The locations of such supports must be chosen so as to minimize the global compliance of the beam. Optimality conditions for this problem are discussed.     

Optimal design of layered structures under dynamic loading

A direct search procedure is presented to treat problems of optimization of layered structures subjected to dynamic loading conditions. The procedure combines the basic idea of the complex method of Box to locate the next trial point, with a local direct pattern search of Hooke and Jeeves to insure the continuous accelerative movement toward the optimum. The method is applied to two problems of optimal design for minimum tensile stress at the interfaces in layered structures under time-harmonic loads and transient loads, respectively.     

Nonlinear analysis of concrete cylinder structures under hydrostatic loading

The paper reports the recent results of four aspects of nonlinear analysis of concrete cylinder structures under hydrostatic loading—(1) further development of concrete constitutive relationships based on a plasticity formulation; (2) kinematics of failure mode for crushing and cracking concrete; (3) implementing the results in the form of a subroutine suitable for incorporation in a large finite-element analysis computer code (NONSAP program); and (4) studying the behaviour and strength of concrete cylindrical shell structures under hydrostatic pressure.The computer model developed includes the nonlinear displacement and material behaviour which is capable of performing parametric studies on the influence of geometric imperfections, variable restrained end supports, nonlinear nature of stress-strain-fracture response, and the non-conservative nature of hydrostatic loading. Using this computer model, comparisons have been made with the results of tests on actual cylinders, providing the needed confirmation of the validity of the model.     

Optimal design of elastic-plastic stepped beams under dynamic loading

The optimal design of two-stepped elastic-plastic beams under dynamic loads is discussed. Such beam dimensions are sought for which a minimum peak deflection is attained within designs of constant volume. The numerical results achieved are compared with results for elastic and rigid-plastic beams obtained in previous papers by the author.     

悬臂式蜂窝夹层板的非线性动力学建模及分析

蜂窝夹层结构因其良好的力学特性,在众多工程领域具有非常广泛的应用.本文建立了悬臂边界条件下,蜂窝夹层板的动力学模型并研究其非线性动力学行为.选取文献中更加接近实体有限元解的等效弹性参数公式对蜂窝芯层进行等效简化,得到六角形蜂窝芯的等效弹性参数.基于Reddy高阶剪切变形理论,应用Hamilton原理建立悬臂式蜂窝夹层板在受到面内激励和横向激励联合作用下的偏微分运动方程.然后利用Galerkin方法得到两自由度非自治常微分形式运动方程.在此基础上,通过对悬臂式蜂窝夹层板进行数值模拟分析系统的非线性动力学.结果表明面内激励和横向激励对系统的动力学特性有着重要影响,在不同激励作用下系统会出现周期运动、概周期运动以及混沌运动等复杂的非线性动力学响应.     

Formulation of Mindlin-Engesser model for stiffened plate vibration

In this paper, a Mindlin-Engesser model is developed for the vibration analysis of moderately thick plates with arbitrarily oriented stiffeners. The theoretical derivation incorporates the Mindlin theory to account for the effects of transverse shear deformation and rotary inertia of plates, and the Engesser theory to account for the shear deformation of stiffeners with the inclusion of torsion effect. In the method of solution, the resulting energy functionals are minimized using the Ritz procedure with a set of admissible two-dimensional functions expressed in the form of simple polynomials. The key kinematic feature of these shape functions is that they are boundary oriented and no boundary losses are introduced as in discretization methods. With the aim of demonstrating the applicability and versatility of the method, numerical examples including plates of various shapes with arbitrarily oriented stiffeners are presented. Several findings and conclusions regarding the method have been highlighted and discussed.     

Static and dynamic analysis of stiffened plates

In this paper a method for the static and dynamic analysis of eccentrically stiffened annular sector plates is presented. The plate is clamped on all the edges. The integral equation technique is adopted for the solution. In the static analysis the deflection and stresses at centre and the stresses at the edges are obtained and they are presented graphically. The results are compared for particular cases with those of other investigators who have used different analytical methods. The natural frequencies of stiffened clamped plates are also obtained for plates with different sector angles.     

Automatic calculation for bending of rigid-plastic beams under dynamic loading

Rigid-plastic stepped beams under impulsive or dynamic pressure loading are considered. The ends of the beam are simply supported, clamped or free. Permanent deflections of the beam are found by the method of mode form motions. For automatic calculation of the deflections a FORTRAN packet of programs DINOPT is put together. Three examples which demonstrate the facilities of this packet are given.     

Reliability analysis of spacecraft structures under static and dynamic loading

The aim of the present paper is to demonstrate that, thanks to recently proposed simulation-based methods, it is now possible to efficiently analyse the reliability of large-scale structures modelled with very large FE systems. This capability is of paramount importance for industrial applications, because the related FE models steadily grow in size and so does the number of model parameters associated with uncertainty. The analysis methods applied in this study belong to the class of advanced Monte-Carlo simulation methods, with which the computational costs induced by direct simulation can be drastically reduced. Based on the theoretical foundations of the methods, which are specifically geared towards problems featuring thousands of parameters affected by uncertainty, the present paper provides the first demonstration that these methods can be used to assess the reliability of complex structural assemblies, even for extremely high levels of reliability.The reliability analysis is performed using a refined finite element model (120,000 DOF) of a satellite, both under static and dynamic loading. For the static load case the reliability can be estimated with great efficiency, whereas for the dynamic load case the performance depends on the considered frequency range. The obtained results are very significant in that they show the feasibility of a full scale analysis of the structural reliability in a design context for large-scale structures.     

压电复合材料悬臂板1∶3内共振的非线性动力学分析

本文以飞行器机翼为工程背景,将机翼简化为悬臂板模型,在应用经典板理论和Hamilton原理建立横向和面内激励共同作用下压电复合材料悬臂板的无量纲非线性偏微分方程的基础上,利用Galerkin方法将系统离散为两自由度的非线性常微分方程.然后考虑主参数共振-1∶3内共振,运用多尺度法将两自由度的系统控制方程进行摄动分析,推导出四维平均方程.基于四阶Runge-Kutta法,使用MATLAB软件研究了横向外激励幅值和压电参数项对压电复合材料悬臂板非线性动力学行为的影响.结果表明,系统存在周期和混沌运动,所得结论对实际工程具有指导意义.     

Optimum design and evaluation of stiffened panels with practical loading

Optimum design of a blade-stiffened panel of composite/honeycomb sandwich construction and a metal T-stiffened panel is considered using the buckling and strength constraint program VICONOPT. Both panels have practical loadings which produce a nonlinear out-of-plane bending moment, calculated using beam-column expressions. Large deflection finite element analysis of the optima shows that modifications to these expressions are necessary when the panels are shear loaded. The use of integrally machined stiffeners, as opposed to a conventional, built-up panel designed using PANDA2, is shown to permit 20% mass saving when the latter has no postbuckling strength and 3% saving when postbuckling strength is allowed for.     

动态加载方式下防爆墙动力响应分析

为分析防爆墙在不同爆炸载荷下的动力响应和破坏机理,研究波纹板式防爆墙与平板式防爆墙的差异,分别采用三角波加载和基于流固耦合方法的爆炸仿真2种动态加载方式模拟爆炸载荷。分析结果表明：三角波载荷可以较好地模拟爆炸载荷且具有明显的计算速度优势。分析得到2种类型防爆墙的P I曲线,通过对比发现波纹板式防爆墙的抗爆性能优于平板式防爆墙。     

Finite-element dynamic inelastic analysis of beams and plates under combined loading

The response of beams and plates under multiple loading is considered taking into account the inelastic interactions between moments and axial (in-plane) forces. The plastic analysis is based on distribution of stresses and strains in three dimensions so that yielding remains a function of the uniaxial state of stress in beams and of the biaxial state of stress in plates. The interaction effects between dynamic transverse loads and static in-plane loads is studied by using initial stress stiffness matrices that modify the original stiffness matrices. Detailed response behavior of beams and plates in combined loading is presented. The response characteristics are found to exhibit interaction instability properties.     

冲击作用下七元石英传感器动态性能研究

石英传感器已被广泛应用于冲击波剖面应力的测量。通过1.16 GPa冲击作用下七元石英传感器与分流型、短路型单元石英传感器的对比实验研究表明:七元石英传感器测量单元的压电电流特征与短路型单元石英传感器基本相同;中心测量单元受边缘效应等因素的影响较小,压电电流斜升幅度相对最小,其性质类似于分流型单元石英传感器,可特别应用于空间非均匀冲击作用分布等的测量。