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Presented in partial fulfillment of the requirements for the Masters Diploma in Technology: Civil Engineering, Technikon Natal, 1993. / M

The analysis of stiffened plate structures subject to complex loads such as air-blast pressure waves from external or internal explosions, water waves, collisions or simply large static loads is still considered a difficult task. The associated response is highly nonlinear and although it can be solved with currently available commercial finite element programs, the modelling requires many elements with a huge amount of input data and very expensive computer runs. Hence this type of analysis is impractical at the preliminary design stage. The present work is aimed at improving this situation by introducing a new philosophy. That is, a new formulation is developed which is capable of representing the overall response of the complete structure with reasonable accuracy but with a sacrifice in local detailed accuracy. The resulting modelling is relatively simple thereby requiring much reduced data input and run times. It now becomes feasible to carry out design oriented response analyses. Based on the above philosophy, new plate and stiffener beam finite elements are developed for the nonlinear static and dynamic analysis of stiffened plate structures. The elements are specially designed to contain all the basic modes of deformation response which occur in stiffened plates and are called super finite elements since only one plate element per bay or one beam element per span is needed to achieve engineering design level accuracy at minimum cost. Rectangular plate elements are used so that orthogonally stiffened plates can be modelled. The von Karman large deflection theory is used to model the nonlinear geometric behaviour. Material nonlinearities are modelled by von Mises yield criterion and associated flow rule using a bi-linear stress-strain law. The finite element equations are derived using the virtual work principle and the matrix quantities are evaluated by Gauss quadrature. Temporal integration is carried out using the Newmark-β method with Newton-Raphson iteration for the nonlinear equations at each time step. A computer code has been written to implement the theory and this has been applied to the static, vibration and transient analysis of unstiffened plates, beams and plates stiffened in one or two orthogonal directions. Good approximations have been obtained for both linear and nonlinear problems with only one element representations for each plate bay or beam span with significant savings in computing time and costs. The displacement and stress responses obtained from the present analysis compare well with experimental, analytical or other numerical results. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

A dissertation submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, in fulfilment of the requirements for the degree of Master of Science in Engineering Johannesburg, 2016 / This dissertation presents a parametric study conducted on the dimensions of an inverted box rib (IBR) sheet. The objectives of the study were (i) to obtain the optimum dimensions that would be used to simulate new IBR profiles made from standard sheet input coils whilst meeting the stiffness criterion; and (ii) to perform a cost analysis to determine the most economic simulated profile. The dimensions which were varied in the parametric study were rib-height, rib-width, sheet thickness and the number of pans per 686 mm cover width of a single IBR 686 sheet. Numerical experiments were conducted using the Finite Elements Method and Abaqus/CAE software. The results were compared to the predictions obtained from Euler-Bernoulli beam theory. The outputs from the experiments were the sheet deflection from which stiffness was determined, and eigenvalues from which the profiles’ stability and buckling modes were calculated. This study found that sheet stiffness increased as the rib-height, sheet thickness and number of pans per 686 mm cover width increased. In contrast, the rib-width had little effect on the sheet stiffness. Hence, it was concluded that, for any IBR sheet profile, the rib-width should be kept at approximately 23 mm to avoid using more material in the sheet. The optimum dimensions found were rib-height of 34 mm, rib-width of 23 mm and four pans per 686 mm cover width. The commercially available IBR 686 sheet is made up of four pans and has a rib-height and a rib-width of 37 and 33 mm, respectively. It is manufactured from an input sheet coil of 925 mm. Reducing the rib-height from 37 mm to 34 mm and the rib-width from 33 mm to 23 mm resulted in increasing the cover width by 8 %. The optimum dimensions were further used to simulate profiles made from the 925, 940, 1000, 1175, 1219, 1225, 1250 and 1320 mm standard sheet coils in order to find the most economic IBR profiles that met the stiffness criterion. The 1250 mm coil yielded the most economical IBR profile, which has six 97 mm wide pans, and a 996 mm cover width. This profile resulted in a 10 % cost saving compared with the next closest profile. / MT2017

Several search methods for unconstrained minimization in the minimum weight design of a stiffened cylindrical shell are investigated. The cylindrical shell, under study, is stiffened with bar shaped stiffeners in the longitudinal and circumferential directions, and capable of being loaded both axially and radially with up to ten separate load conditions. For this investigation, it was necessary to alter an unconstrained minimization program for use on the IBM 360 computer by employing double precision techniques. The computer runs obtained on this system are compared with those provided by the prior work of William Morrow and Lucien Schmit. The results show, as great as, a 7% reduction in the final weight. Either slight alterations in the initial stiffener and cylinder dimensions, or the conversion of the program to double precision is responsible for the change. Regardless of which, the sensitivity or inexactness of the minimization process is apparent.

This dissertation evaluates higher-order modal methods for predicting thermal and structural response. More accurate methods or ones which can significantly reduce the size of complex, transient thermal and structural problems are desirable for analysis and are required for synthesis of real structures subjected to thermal and mechanical loading. A unified method is presented for deriving successively higher-order modal solutions related to previously developed, lower-order methods such as the mode-displacement and mode-acceleration methods. A new method, called the force derivative method, is used to obtain higher-order modal solutions for both uncoupled (proportionally-damped) structural problems as well as thermal problems and coupled (non-proportionally damped) structural problems. The new method is called the force-derivative method because, analogous to the mode-acceleration method, it produces a term that depends on the forcing function and additional terms that depend on the time derivatives of the forcing function. The accuracy and convergence history of various modal methods are compared for several example problems, both structural and thermal. The example problems include the case of proportional damping for: a cantilevered beam subjected to a quintic time varying tip load and a unit step tip load and a muItispan beam subjected to both uniform and discrete quintic time-varying loads. Examples of non-proportional damping include a simple two-degree-of-freedom spring-mass system with discrete viscous dampers subjected to a sinusoidally varying load and a multispan beam with discrete viscous dampers subjected to a uniform, quintic time varying load. The last example studied is a transient thermal problem of a rod subjected to a linearly-varying, tip heat load. / Ph. D.

Traditionally, in reliability design, the random variables acting on a system are assumed independent. This assumption is usually poor because in most real life problems the variables are correlated. The available information, most of the time, is limited to the first and second moments. Very few methods can handle correlation between the variables when the joint probability density function is unknown. There are no reports that provide information of the accuracy of these methods. This work presents an evaluative study of reliability under incomplete information, comparing three existing methods for calculating the probability of failure: The method presented by Ang and Tang which assumes the correlation between the variables to be invariant; Kiureghian and Liu/s method which accounts for the change in correlation and; Rackwitz's method under the assumption of independence. We have also developed a new algorithm to generate random samples of correlated random variables when the marginal distributions and correlation coefficients of these variables are specified. These samples can be used in Monte Carlo simulation which is a tool for comparison of the three methods described above. This Monte Carlo simulation approach is based on the assumption of normal joint probability density function as considered by Kiureghian and Liu. To examine if this approach is biased towards Kiureghian and Liu, a second Monte Carlo simulation approach with no assumption about the joint probability density function is developed and compared with the first one. Both methods that account for correlation show a clear advantage over the traditional approach of assuming that the variables are independent. Moreover, Kiureghian and Liu's approach proved to be more accurate in most cases than Ang and Tang's method. In this study, it is also shown that there is an error in calculating the safety index for correlated variables when either one of the methods in study is implemented, because the joint probability density function of the random variables is neglected. / Master of Science

A user friendly preprocessor was developed and documented for the plane and space frame and space truss structural analysis programs that are based on the matrix displacements method. This preprocessor is comprised of three programs. The main program in the preprocessor is to allow the user to create error free input data files. This program also allows modifications of existing input data files. The two other programs are the library manager and the graphics presentation. The library manager is used to manage the libraries of the element and material properties. The graphics presentation is used to display a plane structure on the graphics display. In Chapter 2, the development of a user friendly preprocessor is discussed. After a short review of the extension of the analysis program from plane frame to space frame in Chapter 3, the preprocessor and its supporting programs are described in detail in the user manual in Chapter 4. Possible extensions to the preprocessor are discussed in Chapter 5. The appendix contains examples of input data files for these structural analysis programs. / Master of Science

When structural analysis is performed via iterative solution technique it is possible to integrate the analysis and design iterations in an integrated analysis and design procedure. The present work seeks to apply an integrated analysis and design approach due to Rizk to the problem of hole shape optimization in thick plates. The plates are modeled by three dimensional eight noded elements. An element by element (EBE) preconditioned conjugate gradient (PCG) method is used for the structural analysis, because this method is well suited for poorly banded three dimensional problems. The plates were optimized so as to minimize the stress concentration near the hole measured by the ratio of the Von Mises stress to the applied boundary stress. The analysis program was validated by comparison to a commercial finite-element program as well as photoelastically obtained stress concentrations. Similarly, the optimization procedure was checked against plates optimized by a photoelastic technique. Good agreement was observed. The integrated analysis and design approach tested here is based on partially converged solutions of the EBE-PCG iterative process. A study of the effect of the number of iterations on analysis and derivative accuracy was performed. Based on this analysis a choice was made for the number of iterations to be used in the integrated analysis and design procedure. It was found that the cost of the design could be significantly reduced with only minimal effects on the final shape and stress concentration factor. / Master of Science

In conclusion, it can be said that the method of approach (whether by the minimum complementary energy or column analogy) is very straightforward, and the final set of equations can be developed very quickly. However, the final simultaneous solution presents a very difficult part of obtaining the final answers. / Master of Science