Vibrations of thick plates using a high precision triangular element

In this paper vibrations of thick plates using a high precision triangular element are studied. The effect of transverse shear is included in the derivation of the stiffness matrix and the effect of rotatory inertia is included in the derivation of the mass matrix of the element. Explicit expressions for stiffness and mass matrices of the element are presented. The numerical examples considered show that the natural frequencies obtained are accurate even with a coarse finite element subdivision.     

A comparative study of variable and constant thickness high precision triangular plate bending elements in the analysis of variable thickness plates

For the analysis of plate bending and vibration problems high precision triangular elements are very attractive. The effect of thickness variation can be included in these elements very easily at the expense of the computer time, for analysing variable thickness plates. On the other hand, variable thickness plates can be analysed as stepped plates with constant thickness elements with less computer time. In this paper a comparative study of the use of variable thickness and constant thickness elements for analysing variable thickness plates is attempted by solving three typical problems. The results show that for static problems there is a marginal accuracy when using variable thickness elements as against average thickness elements. However, for vibration problems even though there is not much difference in the fundamental frequency parameter obtained by using both elements, the higher modes obtained by using variable thickness elements are very accurate.     

Thermal bending of thick rectangular plates

An analysis with a shear deformation capability for the thermal bending of thick rectangular plates is presented. Formulation of the problem, with appropriate thermal terms incorporated and applicable to the bending of moderately thick plates, has been carried out by using Reissner's plate bending theory. Representative plate bending problems have been considered for illustrating the procedure. Numerical results obtained indicate that thick plate solutions to thermal problems deviate from those of the classical theory in practically the same manner as with mechanical loading cases.     

Finite element analysis of thick annular and sector plates

A finite element displacement formulation based on Reissner's thick plate theory is presented for the bending analysis of annular and sector plates. An annular element and an annular sector element, associated with six and twenty degrees of freedom, respectively, are developed. One of the significant features of these elements, which include both bending and shear deformation effects and which conform with respect to all degrees of freedom considered, is the ability to satisfy exactly the condition of vanishing shear stress resultant along a free edge. Numerical results are presented for substantiating the proposed procedure.     

A thick plate model for bending and twisting of CANDU fuel endplates

A finite element model for in-plane bending, out-of-plane bending and twisting of CANDU fuel endplates is developed using Reddy's third-order thick plate theory in this paper. From theoretical considerations, the proposed model is expected to be superior to the beam theories in dealing with the joining of curved rings and straight ribs. Numerical results obtained for test cases show that the plate model presented is efficient and accurate.     

On the convergence of a mixed finite element scheme for plate bending

The convergence of a mixed finite element scheme for plate bending, previously proposed by the present authors, is discussed on the basis of functional analysis. First, the outline of the formulation is presented with some mathematical preliminaries. Then, several kinds of energy inequalities are established to assure the stability of the approximate solution. Thus, the rate of convergence may be obtained by the evaluation of the degrees of the completeness and consistency of the employed shape functions. Some remarks are also given with respect to the extension of the method to initial value problems.     

Three dimensional analysis of thermally loaded thick plates

A mixed three dimensional formulation is presented for the analysis of thermally loaded thick plates. The method developed follows the guidelines furnished by the Vlasov-Iyengar technique applicable to the analysis of mechanically loaded thick plates, in which the three dimensional governing equations are derived from the elasticity equations by using a MacLaurin series approach. The expressions for the components of displacement, stress, and heat flux as well as the temperature are obtained in a series form in terms of the linear partial differential operators operating on a set of initial functions, which are the solutions to the governing equations. The procedure to be followed in arriving at the solution is illustrated by solving the problem of the thermal bending of a clamped-supported thick square plate; it is found that the present solution deviates significantly from those of the lower order theories for large values of the thickness ratio.     

Stability of stiffened plates using high precision finite elements

High precision finite elements for both thin plate and stiffener are developed in this paper to analyse the stability of thin plates subjected to arbitrary membrane loading with arbitrarily oriented stiffeners. Application of these elements to some complex stability problems show high accuracy even with a relatively coarse finite element mesh. For all the problems considered the predicted critical loads are accurate upper bounds.     

Finite element analysis of moderately thick shells

Thick shells of revolution find application in nuclear pressure vessel technology. In this paper, a finite ring shell element, based on the stress-strain relations of moderately thick shells, is developed. The element has 20 degrees of freedom. Cubic polynomials are assumed for all the generalized displacements, i.e. the in-plane forces, the normal displacements and the total rotations of the normal about the co-ordinate lines. This ensures faster convergence and better accuracy in the results. The effectiveness of the element is demonstrated by numerical examples.     

Method of initial functions in the analysis of thick circular plates

The method of initial functions has been used for the analysis of thick circular plates. In this method, the governing equations are derived from the three-dimensional elasticity equations in cylindrical polar coordinates using a Maclaurin series expansion in thickness coordinate for the unknowns. The formulation is in a form which is particularly amenable to consistent reduction to obtain approximate theories of any desired order. Numerical results obtained using this method are compared with those of elasticity solution for the case of a simply supported plate and for a plate subjected to self-equilibrating normal loads. Results are also given for clamped plates subjected to a uniformly distributed load.     

Reduced and selective integration techniques in the finite element analysis of plates

Efforts to develop effective plate bending finite elements by reduced integration techniques are described. The basis for the development is a ‘thick’ plate theory in which transverse shear strains are accounted for. The variables in the theory are all kinematic, namely, displacements and independent rotations. As only C⁰ continuity is required, isoparametric elements may be employed, which result in several advantages over thin plate elements. It is shown that the avoidance of shear ‘locking’ may be facilitated by reduced integration techniques. Both uniform and selective schemes are considered. Conditions under which selective schemes are invariant are identified, and they are found to have an advantage over uniform schemes in the present situation. It is pointed out that the present elements are not subject to the difficulties encountered by thin plate theory elements, concerning boundary conditions. For example, the polygonal approximation of curved, simply-supported edges is convergent. Other topics discussed are the equivalence with mixed methods, rank deficiency, convergence criteria and useful mass ‘lumping’ schemes for dynamics. Numerical results for several thin plate problems indicate the high degree of accuracy attainable by the present elements.     

高精度三维霍尔探头的标定

介绍了在上海光源(SSRF)磁测实验室中,用可旋转标准电磁铁产生均匀磁场,进行霍尔探头的温度、非线性的标定以及平面霍尔效应的研究;解决了测量椭圆极化型波荡器时水平磁场与垂直磁场间相互影响的问题,提高了磁场测量的精度。     

单脉冲磁场精确设定装置的研制

本文介绍了一种用于磁镜装置研究中脉冲磁场精确设定的装置，其重复精度误差小于１／１０００。     

脉冲强磁体中应力的有限元分析

提高脉冲磁场强度的主要障碍是磁体中巨大的应力,而脉冲磁体中应力的产生和作用过程比较复杂,要准确地计算出来很困难。采用有限元法对脉冲磁体中的应力进行分析,计算中全面考虑了预应力、电磁力、热应力等情况。通过计算,得出了,一些设计脉冲磁体的基本原则。     

Finite-element analyses of post-collapse plastic bending of thick pipes

A comparative study of the application of four different types of finite-elements namely elbow (ring), shell, solid, and generalised plane strain to model the post collapse bending behaviour and flow area reduction in an initially straight thick cylindrical pipe made of a highly non-linear material is presented to evaluate their effectiveness. Large strain-large bending FE analyses were performed in each case and the results of moment-curvature relations and pipe-section deformation predictions are compared. The study shows that although solid elements do provide a reasonably accurate and effective solution these are computationally more expensive, while the generalised plane strain finite-elements yield an equally effective and reasonably accurate solution to the problem but are less expensive.     

Post-collapse cross-sectional flattening of thick pipes in plastic bending

Post-collapse cross-sectional flattening of a thick pipe at the centre of a plastic hinge formed during excessive bending due to unrestrained pipe whip is analysed with an aim to ascertain the extent of flow choking and consequent reduction of blowdown force. Based on the experimentally observed similarity between the plastic collapse mode of the critical pipe section during bending and plastic deformation of a ring under lateral compression, the effect of excessive bending on pipe section flattening is simulated using some well known analytical models for section collapse. A theoretical relationship between post-collapse bend curvature and section flattening is proposed for relatively thick pipes made of strain hardening material. The calculations made using the above relationship are found to compare well with those observed experimentally.     

A comparison of closed-form and finite-element solutions of thick laminated anisotropic rectangular plates

In this study the effects of reduced integration, mesh size, and element type (i.e. linear or quadratic) on the accuracy of a penalty-finite element based on the theory governing thick, laminated, anisotropic composite plates are investigated. In order to assess the accuracy of the present finite element, exact closed-form solutions are developed for cross-ply and antisymmetric angle-ply rectangular plates simply supported and subjected to sinusoidally distributed mechanical and/or thermal loadings, and free vibration.     

High precision thick target PIXE analyses of carbonaceous meteorites

High precision proton-induced X-ray (PIXE) thick target spectra of carbonaceous meteorites have been deconvoluted using previously described programs. Even in cases of totally overlapping peaks excellent fits to spectra were obtained. Concentrations for 15 elements in the mass range 56–100, as well as Pb, agree well in most cases with previous literature values. The total concentration range studied was over 10⁵, with the lowest concentrations precisely analyzed being around 1 ppm.     

Proposal of failure criterion applicable to finite element analysis results for wall-thinned pipes under bending load

In this work, a failure criterion applicable to large strain Finite Element Analysis (FEA) results was proposed in order to predict both the fracture mode (collapse or cracking) and the limit bending load of wall-thinned straight pipes. This work was motivated from the recent experimental results of Tsuji and Meshii (2011); that is, fracture mode is not always collapse, and the fracture mode affects the limit bending load. The key finding in comparing their test results and a detailed large strain FEA results was that the Mises stress distribution at the limit bending load of a flawed cylinder was similar to that of a flawless cylinder; specifically, in case of collapse, the Mises stress exceeded the true yield stress of a material for the whole “volume” of a cylinder with a nominal wall thickness. Based on this finding, a failure criterion applicable to large strain FEA results of wall-thinned straight pipes under a bending load that can predict both fracture mode and limit bending load was proposed and was named the Domain Collapse Criterion (DCC). DCC predicts the limit bending load as the lower value of either the M_c^FEA, which is the load at which the Mises stress exceeds the true yield strength of a straight pipe for the whole “volume” with a nominal wall thickness (fracture mode: collapse), or the M_c^FEAb, which is the load at which the Mises stress in a section of the flaw ligament exceeds the true tensile stress (fracture mode: cracking). The results showed that the DCC could predict the fracture mode appropriately and the experimental limit bending load fundamentally on the conservative side within a maximum 20% difference regardless of the fracture mode. Another advantage of the DCC is that it uses the true yield and true tensile strength as the critical strength of the material and not the ambiguous flow strength.     

Limit loads of variable thickness circular plates in bending

This paper presents the results of an investigation of rigid-plastic collapse of simply supported circular plates of variable thickness. The plates are loaded with a uniformly distributed transverse pressure and the material is assumed to yield according to the von Mises criterion. Numerical results for collapse loads and stress fields are given in graphs and the solution for the resulting velocity fields is indicated.