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.     

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 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.     

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.     

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.     

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.     

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.     

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。     

Topology optimization of nonlinear structures with damping under arbitrary dynamic loading

This study presents an extended unit load method in which the displacement of a chosen degree of freedom (DOF) in a nonlinear structure under arbitrary dynamic loading is expressed as an integration of mutual strain energy density over a continuum domain. This new integral formulation for the displacement of a chosen DOF is developed by using the virtual work principle and can be used for linear or nonlinear structural behaviours. The integral form of the displacement is then used to develop new formulations for structural topology optimization involving arbitrary dynamic loading using the moving iso-surface threshold (MIST) method. Presented are two specific topology optimization problems with two objective functions: (a) to minimize the peak of a chosen displacement; or (b) to minimize the average power spectral density (PSD) of the chosen displacement over a finite time interval. New MIST formulations and algorithms are developed for solving two damping topology optimization problems of a structure under arbitrary dynamic loading, with or without large displacements, and having cellular damping materials with multi-volume fractions. Several numerical examples are presented to demonstrate the validity and efficiency of the presented unit load method and the MIST formulations and algorithms.     

Localisation in a Cosserat continuum under static and dynamic loading conditions

Localisation studies have been carried out for an unconstrained, elasto-plastic, strain-softening Cosserat continuum. Because of the presence of an internal length scale in this continuum model a perfect convergence is found upon mesh refinement. A finite, constant width of the localisation zone and a finite energy dissipation are computed under static as well as under transient loading conditions. Because of the existence of rotational degrees-of-freedom in a Cosserat continuum additional wave types arise and wave propagation becomes dispersive. This has been investigated analytically and numerically for an elastic Cosserat continuum and an excellent agreement has been found between both solutions.     

Nonlinear finite element analysis of reinforced concrete plates and shells under monotonic loading

Plane stress constitutive models are proposed for the nonlinear finite element analysis of reinforced concrete structures under monotonic loading. An elastic strain hardening plastic stress-strain relationship with a nonassociated flow rule is used to model concrete in the compression dominating region and an elastic brittle fracture behavior is assumed for concrete in the tension dominating area. After cracking takes place, the smeared cracked approach together with the rotating crack concept is employed. The steel is modeled by an idealized bilinear curve identical in tension and compressions. Via a layered approach, these material models are further extended to model the flexural behavior of reinforced concrete plates and shells. These material models have been tested against experimental data and good agreement has been obtained.     

Nonlinear dynamic characteristics of piezoelectric bending actuators under strong applied electric field

Dynamic characteristics of piezoelectric bending actuators under low and high electric fields are studied using the asymptotic theory of nonstationary vibrations. The proposed nonlinear model predicts the changes in fundamental resonant frequencies of the piezoelectric cantilever. The predicted resonance amplitude of the tip deflections of the piezoelectric actuators, which increases with the increase in the magnitude of the electric field, well agrees with the experimental results. Additionally, the decrease in the mechanical quality factor with the increase in the electric field, the tip deflection of piezoelectric actuators near resonance frequency,and the amplitude of the tip deflection at the fundamental vibration tone under an applied electric field varying with time have also been obtained using the present model.     

Weight optimization of stiffened cylinders under axial compression

A procedure is developed for the design of a stiffened cylinder under a given uniform axial compression with minimum weight. The approach allows the consideration of various shapes of stiffening members. The effective stiffness of the skin in its post-buckled state is taken into account in the basic analysis. The buckling analyses are accomplished as a minimum problem in the buckling mode shape parameters space using the variable metric method. A mixed procedure which combines the exterior penalty function concept and random search is used to minimize the weight of the stiffened cylinders. The design examples demonstrate the validity of the present approach.     

Weight optimization of stiffened cylinders under axial compression

A methodology is developed, by which one may design a stiffened cylinder of specified material, radius, and length, such that it can safely carry a given uniform axial compression with minimum weight. The solution procedure is divided into two stages, Phase I and Phase II. In Phase I, an unconstrained minimization is performed against one of the active constraints (in this paper-general instability) and data are generated in a sufficiently large region of the design space by employing efficient mathematical search techniques, in Phase II, these data are employed to arrive at the minimum weight configuration that satisfies all other constraints. Two design examples are presented which demonstrate the methodology.