Nonlinear Analysis of TREAT MK III Loop

Earthquakes have occurred for millions of years and will continue in the future affecting millions of lives, thousands infrastructure and costing billions of dollars. Seismic soil structure interaction is the process in which the structure rested on the ground and subjected to an earthquake is affected by the response of the soil medium beneath it having its own characteristics. Thus, soil structure interaction response is dictated by the interaction between the structure, foundation and underlying soil or rock. To clarify the contribution of the seismic soil structure interaction, 3D time history finite element models of 15 story concrete frame building were performed using Abaqus under Kocaeli’s Mw = 7.5 strong ground motion. The effects of soil boundary limits, mat thickness and soil linearity were investigated. To demonstrate the importance of modeling correct soil structure interaction problems, the numerical analysis was carried out for three cases: (1) a fixed-base structure, (2) a structure rested on silty sandy soil, and (3) a structure supported by raft foundation and rested on silty sandy soil. The results, presented in terms of the structural lateral deflection and base shear versus time, show that soil structure interaction effects should be evaluated when the maximum lateral deflection is obtained at top of the structure regardless when it occurred as well as at maximum absolute lateral deflection at each level. Moreover, excluding soil structure interaction effects may result in inadequate structural safety for the frame building rested on silty sandy soil and considering linear soil properties may result in non-economical structural design.

Analysis and design of eccentrically compressed ultra-high-strength slender CFST circular columns

Evaluation of excessive wellhead motions: Reliability assessment and wellhead integrity index (Part II)

Efficient large deflection analysis of rectangular orthotropic plates by direct energy minimisation

Stress–strain analysis of a cylindrical pipe subjected to a transverse load and large deflections

An analytical closed-form expression is derived for the shear correction factor of beams with annular cross sections. The beam theory is formulated using the variational asymptotic method, which uses inherently occurring small parameters to convert a variational statement from three-dimensional elasticity to an engineering beam theory without any ad hoc assumptions on the beam kinematics. Comparisons are made with existing solutions in the literature; then, the critical speeds of a rotor are shown to depend not only on the inclusion of transverse shear but also on the choice of the shear correction factor, establishing its importance. The motivation of this work is twofold: first, rotors that can be modeled as beams with annular cross sections are often encountered, and this expression for the shear correction factor can be readily incorporated into any rotor dynamics solver; and second, closed-form expressions, when available, always provide more insight into structural mechanics as opposed to numerical solutions.

BackgroundIntegrated proton therapy - MRI systems are capable of delivering high doses to the target tissues near sensitive organs and achieve better therapeutic results; however, the applied magnetic field for imaging, influences the protons path, changes the penetration depth and deflects the particles, laterally, leading to dose distribution variations.ObjectiveTo determine the effects of a magnetic field on the range and the lateral deflection of protons, analytically.MethodsAn analytical survey based on protons energy and range power law relation, without using small angle assumption was done. The penetration depth and lateral deflection of protons with therapeutic energy ranges 60–250 MeV in the presence of uniform magnetic fields of 0–10T intensities, were calculated analytically. Calculations were done for relativistic conditions with Mathematica software version 7.0, and MATLAB 7.0 was applied to plot curves and curve fittings.ResultsIn the presence of a magnetic field, the depth of Bragg peak was decreased and it was shifted laterally. A second order polynomial model with power equation for its coefficients and a power model with quadratic polynomial coefficients predicted the maximum lateral deflection (ymax) and maximum penetration depth (zmax) variations with energy and magnetic field intensity, respectively.ConclusionThe applied correction for deflection angle will give more reliable results in initial energy of 250 MeV and 3T magnetic field intensity. For lower energies and magnetic field intensities the differences are negligible, clinically.

The purpose of this study is to analyze the large deflection problem of bimodular functionally graded truncated thin conical shells under the transverse mechanical load and non-uniform thermal load, in which two different boundary constraints of the truncated shell with two ends simply supported and fully fixed are considered. It is assumed that the temperature distribution along the thickness direction satisfies the Fourier law of heat transfer, and the material properties change exponentially along the thickness direction while different properties in tension and compression are considered. The geometric equation of the conical shell is established based on the equivalent method of curvature correction of von-Kármán deformation theory, and the analytical solution of the problem is obtained by Ritz method. Numerical simulation of bimodular functionally graded conical shells under the thermal and mechanical loads is carried out by Abaqus, and the numerical solution agrees with the theoretical solution. The results show that the introduction of bimodular functionally graded material will affect the maximum displacement and this effect has different rules under the mechanical load and thermal load. In addition, factors such as the cone apex angle and the truncated distance have a great influence on the maximum displacement and its location of the conical shell.

The major assumption of the analysis of plates with large deflection is that the middle surface displacements are not zeros. The determination of the middle surface displacements, u0 and v0 along x- and y- axes respectively is the major challenge encountered in large deflection analysis of plate. Getting a closed-form solution to the long standing von Karman large deflection equations derived in 1910 have proven difficult over the years. The present work is aimed at deriving a new general linear and nonlinear free vibration equation for the analysis of thin rectangular plates. An elastic analysis approach is used. The new nonlinear strain displacement equations were substituted into the total potential energy functional equation of free vibration. This equation is minimized to obtain a new general equation for analyzing linear and nonlinear resonating frequencies of rectangular plates. This approach eliminates the use of Airy’s stress functions and the difficulties of solving von Karman's large deflection equations. A case study of a plate simply supported all-round (SSSS) is used to demonstrate the applicability of this equation. Both trigonometric and polynomial displacement shape functions were used to obtained specific equations for the SSSS plate. The numerical results for the coefficient of linear and nonlinear resonating frequencies obtained for these boundary conditions were 19.739 and 19.748 for trigonometric and polynomial displacement functions respectively. These values indicated a maximum percentage difference of 0.051% with those in the literature. It is observed that the resonating frequency increases as the ratio of out–of–plane displacement to the thickness of plate (w/t) increases. The conclusion is that this new approach is simple and the derived equation is adequate for predicting the linear and nonlinear resonating frequencies of a thin rectangular plate for various boundary conditions.

The mechanical behaviors of the clamped laminated arch with temperature-dependent material properties under the thermal and mechanical loadings are studied in this paper. An analytical method based on the theory of thermoelasticity is proposed for predicting the exact solutions of stresses and displacements in the arch with arbitrary thickness and layer numbers. The clamped support is equivalent to a simply support with a support reaction with the unit pulse function and the Dirac function. The space state method is utilized to establish the state equation by employing the displacements and stresses as the state variables. A slice model is introduced to simplify the coefficient matrix. Based on the continuities at the interfaces, the displacement and stress relationships between the internal and external surfaces of the laminated arch are derived with the transfer matrix method. Exact solutions for the displacements and stresses can be obtained according to the stress boundary conditions on the surfaces of the laminated arch. Finally, convergence and comparison studies demonstrate the excellent efficiency and accuracy of the present method. The influences of material dependency with temperature, thermal load, and thickness-to-radius ratio on the distributions of displacements and stresses are discussed in detail.

ABSTRACTIn this study, a locking-free six-node triangular shell element is proposed to nonlinear analysis of shell structures under the effects of both thermal and mechanical loads. Total Lagrangian formulation is used to consider large deflections and rotations. Besides, mixed interpolation of tensorial components is applied in the relations to deviate shear and membrane locking. The effects of temperature on the nonlinear deflections of shells are studied in several numerical examples. Moreover, analytical solution will be proposed for large deflection analysis of cantilever and simply supported beam under the thermal loads. To validate the proposed formulation, the finite element analysis results are compared by analytical solutions. Based on the obtained results of linear and nonlinear problems, it will be depicted that the authors’ scheme is capable for thermomechanical analysis of shell structures accurately.

A combined theoretical and experimental stress analysis was performed on a bellows to determine if it was suitable for use in absorbing the differential expansion between the shell and tubes of the intermediate heat exchanger for the Hallam Nuclear Power Facility (HNPF). Modes of deformation imposed, singly and in combination, upon a prototype bellows at room temperature included axial deflection, lateral deflection, angular rotation, torsional rotation, and pressurization. Good agreement was obtained between predicted and observed strains. All subsequent tests were performed with Na at 75 psig and 1000 deg F inside the bellows. During the first series of these tests, which simulated the cycling effects of 20 years of normal reactor operation, negligible damage occurred in the bellows. The second series of tests, with Na at 75 psig and 1000 deg F, showed that the bellows could withstand the large axial deflections which might occur during abnormal conditions involving failure of a pump in either the primary or secondary cooling system. In the final series of tests, the axial deflection stroke was gradually increased in a deliberate attempt to induce failure in the bellows. When the stroke was increased to approximately 30 times that expected during normal operation, a reproducible signal was obtained indicating that Na had leaked through the inner ply of the double-ply wall. Even at that time, there was no leakage of Na through the outer ply and the bellows still remained functional. It was concluded that the bellows is well suited for application in the HNPF intermediate heat exchanger. (auth)

A mathematical model was suggested for calculating the mixing process performed by gas bubbling. The adequacy of the model for an apparatus of annular cross section with gas feeding through a nozzle of small diameter was confirmed experimentally. The parameters of the model in relation to the flow rate of the gas fed for mixing were determined. The suggested approaches associated with mixing intensification can find use in spent nuclear fuel reprocessing and in other processes occurring in gas–liquid and liquid–solid heterogeneous systems.

Non-linear bending of antisymmetric angle ply laminated plates

既設構造物等に近接した深い掘削において, 土留め壁の水平変位および周辺地盤における地表面沈下等がどの程度発生するかを影響解析するために土の構成則を考慮した数値解析などが行われるが, より簡便な手法による変位の概略値推定も望まれている。本論文では, 既往計測結果等をもとに地盤および施工条件を勘案した係数の相関から, 深い掘削における地下連続壁の最大水平変位を簡便に推定する手法を提案する.