Arturs Kalnins

Axisymmetric Postbuckling and Nonsymmetric Buckling of a Spherical Shell Compressed Between Rigid Plates

Presents an analysis of the stresses and deflections produced during axisymmetric postbuckling and determines the deformation states at which the shell may buckle into a nonsymmetric shape. The analysis accounts for finite deflections and rotations, but assumes that the material remains linearly elastic throughout the deformation. An experiment shows that both the primary axisymmetric bifurcation point and the secondary nonsymmetric bifurcation point are stable for a shell with R/h approximately equal to 40.

Dynamic buckling of shells: Evaluation of various methods

Abstract The problem of dynamic stability is substantially more complex than the buckling analysis of a shell subjected to static loads. Even at this date suitable criteria for dynamic buckling of shells, which are both logically sound and practically applicable, are not easily available. Thus, a variety of analyses are available to the user, encompassing various degrees of complexity, and involving a range of simplifying assumptions. The purpose of this paper is to compare and evaluate some of these solutions by applying them to a specific problem. A shallow spherical cap, subjected to an axisymmetric, uniform-pressure, step loading, is used as the structural example. The predictions, by various methods, of the dynamic buckling of this shell into unsymmetric modes, are then investigated and compared. The approximate methods used by Akkas are compared to the more rigorous and general solutions of the KSHEL, STARS, DYNASOR, and SATANS computer programs, and the various simplifying assumptions utilized are evaluated. Also included in the comparisons, are the predictions of the relatively simple “dynamic buckling model” approach of Budiansky and Hutchinson. The approaches utilized by the more complex programs [KSHEL (spatial integration, modal superposition, perturbation approach), DYNASOR (finite elements, time integration of non-linear dynamic equilibrium equations), SATANS (finite differences, pseudo load method, time integration), STARS (spatial and time integration, non-linear equilibrium or perturbation approaches)] will in turn be compared in terms of accuracy, idealization complexity, ease of use, and user expertise and experience required for analysis. The comparisons show that the more approximate methods underpredict the dynamic buckling loads for this problem. In addition, some basic assumptions of the simpler solutions are found to be invalid.

Large elastic deformations of shells with the inclusion of transverse normal strain

Abstract For large, elastic deformations and incompressible materials, the thickness of a shell must change when the shell is being stretched. In this paper, a theory of shells is given which admits a prescribed thickness change on the boundaries of the shell and is capable of predicting a symmetric thickness change throughout the shell. The governing equations are written for an incompressible material with a Mooney-type constitutive law.

Free vibration analysis of cylindrical liquid storage tanks

Abstract The circular cylindrical tank, built on grade and usually constructed in steel, aluminum or prestressed concrete, is one of the most common forms of liquid storage vessels. This paper summarizes the results of a comprehensive, computer based, numerical investigation of lateral free vibration of cylindrical liquid storage tanks. An analytical procedure which accurately predicts the fundamental frequencies (corresponding to axial wave number and circumferential wave number both equal to one) of a wide range of cylindrical storage tanks is developed. The procedure is applicable to tanks both completely full and partially full with liquid. Several numerical examples are presented which illustrate application of the procedure and verify its accuracy.

Free vibration analysis of circular cylindrical shells

Abstract Determination of the vibrational characteristics of circular cylindrical shells often requires significant computational effort. This paper presents the results of a comprehensive, computer based, numerical investigation of the free vibration of circular cylindrical shells. An analytical procedure which accurately predicts the natural frequencies and radial mode shapes (corresponding to axial wave number and circumferential wave number both equal to one) for a wide range of circular cylindrical shells is developed. The procedure is applicable to shells either with or without a top closure. Several numerical examples are presented which illustrate application of the procedure and verify its accuracy.

Vibration and stability of prestressed shells

Abstract Thin shells are widely used structural elements and are sometimes subjected to time-dependent loads after they have already acquired some prestress. The response of such a shell can be very different from that when the prestress is absent. The general methods of calculation of the response of the shell are discussed. The stability limit of the shell is viewed as a special result obtained in the free vibration analysis. An example of a typical containment shell of a nuclear power plant, housing the reactor, is worked out in detail.

Seismic analysis of thin shell structures

Abstract We consider in this paper a vertically erected, axisymmetric shell, resting on a horizontal foundation. The foundation is subjected to a time-dependent motion in both the vertical and horizontal directions. The motion may be produced by an event such as an earthquake or explosion. An estimate of the response of the shell to such excitation can be obtained from the solution for time-dependent boundary conditions. This solution is adapted here for an analysis with the response spectrum of earthquakes, which has been pioneered by Biot and Housner. The modes of free vibration are calculated by the multisegment, direct numerical integration method using classical shell theory. An actual design case of a containment vessel of a nuclear power plant built in the US is presented. An estimate of the dynamic response of the shell to an earthquake is obtained for all the relevant variables, such as stresses and displacements. As an example, an estimate for the axial stress of the response is given at various stations of the shell.

Using the Nonlinear Kinematic Hardening Material Model of Chaboche for Elastic–Plastic Ratcheting Analysis

Commonly used design codes for power plant components and pressure vessels include rules for ratcheting analysis that specify limits on accumulated strain. No guidance is provided on the use of the material model. The objective of the paper is to provide guidance that may be helpful to analysts. The Chaboche nonlinear kinematic (NLK) hardening material model is chosen as an appropriate model. Two methods are selected for its calibration that can determine the parameters for stainless steels. One is manual that requires no outside software and the other uses finite element software. Both are based on the monotonic stress–strain curve obtained from a tension specimen. The use of the Chaboche parameters for cases when ratcheting is caused by cyclic temperature fields is selected as the example of an application. The conclusion is that the number of allowable design cycles is far higher when using the parameters with temperature dependency than those at the constant maximum temperature that is being cycled.

Fatigue Analysis in Pressure Vessel Design by Local Strain Approach: Methods and Software Requirements

The purpose, methods for the analysis, software requirements, and meaning of the results of the local strain approach are discussed for fatigue evaluation of a pressure vessel or its component designed for cyclic service. Three methods that are consistent with the approach are evaluated: the cycle-by-cycle method and two half-cycle methods, twice-yield and Seegers. For the cycle-by-cycle method, the linear kinematic hardening model is identified as the cyclic plasticity model that produces results consistent with the local strain approach. A total equivalent strain range, which is entered on a material strain-life curve to read cycles, is defined for multiaxial stress situations .

Contact pressure in rolled tube-tubesheet joints

Abstract The residual contact pressure in a rolled tube-tubesheet joint is calculated for several practical tube-tubesheet size and material selections. The analysis follows the elastic-plastic strain history during the tube expansion process. It accounts also for the initial gap size, reversed yielding, and material strain-hardening of both the tube and the tubesheet. The residual contact pressure is expressed as a function of the degree of expansion of the tube. The inside diameter of the tube after rolling (apparent wall reduction) is chosen as the measure of the expansion. Plots of the residual contact pressure versus the apparent wall reduction show that in all cases the contact pressure attains most of its value within 3–6% of the apparent wall reduction. Further rolling is of no benefit to the residual contact pressure.