Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1994. / Vita. Abstract. Includes bibliographical references (leaves 69-72). Also available via the Internet.

Neste trabalho são descritas análises estática e dinâmica em regime elástico de pórticos espaciais com incerteza no carregamento utilizando o método de elementos finitos (MEF). A abordagem do problema dinâmico estrutural de vibrações forçadas será feita dentro do regime elástico linear com amortecimento viscoso. O pórtico é abordado com teoria de viga fina onde são considerados os acoplamentos devido às forças normais e a torção sobre o modelo de flexão em viga fina de Bernoulli-Euler. A formulação forte do problema dinâmico da viga com carga axial é obtida a partir das equações de equilíbrio de Euler-Lagrange, decorrentes do princípio variacional de Hamilton e, a formulação forte do problema dinâmico do eixo longo sujeito a torção é determinada utilizando o modelo de torção de Saint-Venan. Para a determinação da formulação fraca para o elemento de viga tridimensional foi aplicado o método dos resíduos ponderados Galerkin. Também é descrita neste trabalho, a análise da confiabilidade estrutural considerando a incerteza no carregamento e, em algumas propriedades mecânicas dos materiais, utilizando o método de Monte Carlo (MMC). A série de Neumann foi utilizada como alternativa para reduzir o tempo de processamento do problema dinâmico. A análise simultânea das diversas variáveis foi abordada utilizando a estatística multivariada. Os resultados da analise estática e de vibrações livres dos exemplos numéricos são apresentados com o intuito de validar os métodos contidos neste trabalho comparando-os com resultados obtidos utilizando um software comercial de análise estrutural. / Submitted by Ana Guimarães Pereira (agpereir@ucs.br) on 2015-11-23T16:10:16Z No. of bitstreams: 1 Dissertacao Samuel Cornelli.pdf: 2680799 bytes, checksum: bcb4daa1a00ba8c03aafdea11fa42778 (MD5) / Made available in DSpace on 2015-11-23T16:10:16Z (GMT). No. of bitstreams: 1 Dissertacao Samuel Cornelli.pdf: 2680799 bytes, checksum: bcb4daa1a00ba8c03aafdea11fa42778 (MD5) / In this thesis, static and dynamic analysis of elastic space frames with regime uncertainty in loading using the finite element method (FEM) are described. A structural approach to the dynamic problem of forced vibrations will be made within the linear elastic regime with viscous damping. The structure is approached with thin beam theory which the couplings are considered normal forces due to twisting and bending about the model thin Bernoulli-Euler beam. The strong formulation of the dynamic problem of the beam with axial load is obtained from the equilibrium equations of Euler-Lagrange equations arising from the variational principle of Hamilton and the strong formulation of the dynamic problem of the long shaft under torsion is determined using the model of twist of Saint-Venan. To determine the weak formulation for three-dimensional beam element applies the Galerkin method of weighted residues. Is also described in this study, the analysis of structural reliability considering the uncertainty in loading and some mechanical properties of materials using the Monte Carlo method (MMC). Neumann series will be used as an alternative to reduce the processing time of the dynamic problem. The simultaneous analysis of several variables is addressed using multivariate statistics. Some results of numerical examples are presented in order to validate the methods contained in this work compared with the results obtained from structural analysis of commercial software.

Neste trabalho são descritas análises estática e dinâmica em regime elástico de pórticos espaciais com incerteza no carregamento utilizando o método de elementos finitos (MEF). A abordagem do problema dinâmico estrutural de vibrações forçadas será feita dentro do regime elástico linear com amortecimento viscoso. O pórtico é abordado com teoria de viga fina onde são considerados os acoplamentos devido às forças normais e a torção sobre o modelo de flexão em viga fina de Bernoulli-Euler. A formulação forte do problema dinâmico da viga com carga axial é obtida a partir das equações de equilíbrio de Euler-Lagrange, decorrentes do princípio variacional de Hamilton e, a formulação forte do problema dinâmico do eixo longo sujeito a torção é determinada utilizando o modelo de torção de Saint-Venan. Para a determinação da formulação fraca para o elemento de viga tridimensional foi aplicado o método dos resíduos ponderados Galerkin. Também é descrita neste trabalho, a análise da confiabilidade estrutural considerando a incerteza no carregamento e, em algumas propriedades mecânicas dos materiais, utilizando o método de Monte Carlo (MMC). A série de Neumann foi utilizada como alternativa para reduzir o tempo de processamento do problema dinâmico. A análise simultânea das diversas variáveis foi abordada utilizando a estatística multivariada. Os resultados da analise estática e de vibrações livres dos exemplos numéricos são apresentados com o intuito de validar os métodos contidos neste trabalho comparando-os com resultados obtidos utilizando um software comercial de análise estrutural. / In this thesis, static and dynamic analysis of elastic space frames with regime uncertainty in loading using the finite element method (FEM) are described. A structural approach to the dynamic problem of forced vibrations will be made within the linear elastic regime with viscous damping. The structure is approached with thin beam theory which the couplings are considered normal forces due to twisting and bending about the model thin Bernoulli-Euler beam. The strong formulation of the dynamic problem of the beam with axial load is obtained from the equilibrium equations of Euler-Lagrange equations arising from the variational principle of Hamilton and the strong formulation of the dynamic problem of the long shaft under torsion is determined using the model of twist of Saint-Venan. To determine the weak formulation for three-dimensional beam element applies the Galerkin method of weighted residues. Is also described in this study, the analysis of structural reliability considering the uncertainty in loading and some mechanical properties of materials using the Monte Carlo method (MMC). Neumann series will be used as an alternative to reduce the processing time of the dynamic problem. The simultaneous analysis of several variables is addressed using multivariate statistics. Some results of numerical examples are presented in order to validate the methods contained in this work compared with the results obtained from structural analysis of commercial software.

This dissertation presents new concepts and methodology in designing shape-morphing structures using bistable elements. Developed using the Pseudo-Rigid-Body Model (PRBM), linear bistable compliant mechanism elements produce predictable and controllable length changes. Step-by-step design procedures are developed to guide the design process of these bistable elements. Two different examples of Shape-Morphing Space Frames (SMSFs) were designed and prototyped utilizing the bistable linear elements in a single-layer grid, in addition to flexures and rigid links, to morph a cylindrical space frame into both a hyperbolic and a spherical space frame. Moreover, bistable unit-cell compliant-mechanism elements were also developed to morph a compact structure from a specific initial shape to a final specific shape. The detailed design of those unit cells were done using Computer-aided design (CAD) software following a novel design procedure to transform a one-degree-of-freedom mechanism into a structure with sufficient compliance within its links to toggle between two chosen stable positions. Two different design examples were investigated in this research and prototyped to demonstrate the ability to morph disks into a hemisphere or a sphere with the structure being stable in both states (disk and sphere).

Recent demands in large space structure technology have suggested the use of active control actuators integral to a structures' construction. The concept of a 3-D (triangular cross-sectioned) active truss is presented. The linear equations of motion for one plane of the truss are derived. A model for a generic flexible beam is then appended to the planar truss model. A linear time-invariant optimal control law is found, followed by a presentation of an experimental planar truss built to test the concept. Physical parameters are then substituted into the dynamic model and several sets of control gains are found. The "Kalman'' gains are applied to the experimental structure. Experimental results are compared to expected theoretical results with good (30%) correlation. Conclusions are drawn and suggestions are made for further research. / Master of Science

In order to provide a realistic and challenging experimental test for active vibration control concepts applicable to large space structures, an experimental model is required that simulates the complicated dynamic characteristics of such structures. This study presents the design, theoretical analysis, and experimental testing of such a model - a large, flexible plane grillage, with an adjustable skew angle, free to rotate on knife edges. The plane grillage model was shown, by theory and experiment, to have high modal density at low frequencies (twelve modes below 11 Hz). It was also demonstrated, by analogy with published results for a cantilevered skew plate, that the model would have a pair of closely spaced modes, with distinct mode shapes, at a particular skew angle. By using an ana1ogy with a simple rigid bar model, the pendulum mode of the plane grillage was shown to have a frequency that could be driven towards zero, thereby simulating a rigid body mode. The theoretical analysis was conducted, for one skew angle, using MSC/NASTRAN, and included the effect of gravity. Experimental tests were conducted on the model, with the same skew angle, using frequency and transient response techniques. The theoretical and experimental results were compared, with good quantitative agreement for the natural frequencies (first ten modes within 10%), and reasonable qualitative agreement for the lower mode shapes. / M.S.

Surface errors on parabolic reflector antennas degrade the overall performance of the antenna. They cause amplitude and phase errors in the aperture field which lower the gain, raise the side lobes, and fill in the nulls. These are major problems in large ->space reflector antenna systems. F or example, future multiple beam antenna systems requiring spatial isolation to allow frequency reuse could be rendered useless if high side lobes are present. Space antenna structures are difficult to build. They must maintain a nearly perfect parabolic shape in a harsh environment while remaining lightweight. The restrictions on the structure become more severe as science and technology requirements demand electrically large antennas. Mechanically, there are technologies [4)r building antennas with adaptive surfaces that can compensate for many of the larger distortions caused by thermal and gravitational forces. However, as the frequency and size of the reflectors increase, the subtle surface errors become significant and degrade the overall radiation pattern. It is for this reason that another method must be used to further improve the radiation pattern. Electromagnetic compensation for surface errors in large apace reflector antennas has been the topic of several research studies. Most of these studies try to correct the focal plane fields of the reflector near the radiation pattern. The compensation is implemented by weighting the elements of an array feed. In most of the studies, a precise knowledge of the reflector surface is required. An alternative approach to electromagnetic compensation is presented in this study. The proposed technique uses pattern synthesis to compensate for the surface errors. It differs from previous methods in two major respects. The previous studies used global algorithms that try to correct the entire focal plane field near the focal point or the aperture plane field and, hence, modify the entire radiation pattern. The pattern synthesis approach uses a localized algorithm in which pattern corrections are directed specifically towards portions of the pattern requiring improvement. The second major difference is that the pattern synthesis technique does not require knowledge of the reflector surface, but instead uses radiation pattern data to perform the compensation. / Ph. D.

Space structures are inevitable while covering large spans. Space structures are skeletal structures, which are lighter for the same stiffness when compared with RCC roofs. Till now, space structures, like any other metal structures have been designed assuming the joints as rigid, although there have been several publications about semi rigid joints. Of course, the publications mostly deal with 2D structures and there are very few reports on 3D structures. Space structures, by their nature fall into the latter category. The joints in a space structure are popularly called as "nodes". Generally, nodes, which ensure concentricity of member axes, are either solid or hollow. These are either cast or forged. There are other proprietary types, which do not come under the above classification, and have not been considered in this thesis. Hollow nodes are obviously more economical than solid nodes, but also more flexible. While it is prudent to prefer hollow nodes, it is equally necessary to assess their flexibility, because of its influence on the behaviour of the structure. The hollow spherical node is very popular because of its simplicity and adaptability to various forms of space frames. Double layer grids, which are the most popular forms for roofing applications, are being increasingly implemented. While the hollow spherical node is well suited for double layer grids, an evolutionary development has been what is called as the hollow octahedral node (this node is simply referred to as the 'Octa ' node in this thesis). Chapter 1 introduces space frames and double layer grids in particular, with the advantages of using double-layer grids. Jointing systems available around the world are briefed and the node connector used in the present study is introduced with a brief write-up on its advantages and disadvantages. This chapter also explores the available literature and, the scope and objectives of the thesis are mentioned. Chapter 2 introduces 3D finite element models of the hollow spherical and octahedral nodes. The stiffness matrixes of these nodes have been derived by conducting analyses on the computer for six sizes each of the Octa and spherical nodes. Using the stiffness matrix of the node, a new method of incorporating this into the regular analysis of a space truss has been developed. The new method proposed yields realistic values for the forces in the members and takes into account the elastic deflections in the node under the action of member forces. Implementation of the proposed method has been carried out by writing a custom program using state-of-the-art object oriented programming techniques. A sample problem has been analyzed using this program to demonstrate the effect of including joint flexibility. The effect of flexibility of nodes on the effective length of compression members in double-layer grids has been evaluated. The effect of compliance on the dynamic characteristics of a space frame has also been evaluated for the sample space frame with flexible joints. The analysis program has been modified to evaluate the natural frequencies of the system using rigid or flexible nodes. The study of the Octanode and spherical node under the action of uniaxial compression and tension dominates the contents of Chapter 3. The two types of nodes have been analyzed using commercially available finite element software considering material nonlinearity. The stress patterns from the analyses have been examined thoroughly. Two consistent methods for fixing the load at yield in both uniaxial compression and tension have been proposed using the load-displacement curve. Yield loads for all the nodes have been evaluated using both the methods and the results agree well between the two methods. Three material yield values have been selected for each of the node size for evaluating the yield values viz. 240,320 and 415 MPa. The members of a double layer grid are connected to the nodes by bolts and holes are drilled in the nodes for this purpose. The bolthole patterns differ between two popular types of double-layer grids. Both these bolthole patterns have been modeled separately in the above exercise and the results for these two have been shown to be approximately the same. The effect of varying diameters of the boltholes on the response of the nodes has been examined. Relationships between the yield load, diameter, thickness and material yield have been developed using the method of least squares. The differences in the behaviour of the nodes under uniaxial compression and tension have been discussed. Ramberg Osgood type of relationships have been worked out for all the load-displacement curves obtained from the analyses. The simulation of non-linear behaviour of nodes with cracks with plastic crack closing forces have been carried out with useful insights into the behaviour of the two types of nodes in uniaxial compression and tension. Chapter 4 is devoted largely for studying the two types of nodes under the influence of biaxial load combinations. The combinations studied are dual compression, dual tension and compression-tension. In all cases equal loads are applied along two orthogonal; directions in the horizontal plane. Stress patterns have been examined for each type of load combination and yield values for each case have been obtained using one of the methods proposed in chapter 3. These have been compared with the corresponding uniaxial values in both compression and tension. Some useful inferences have been possible by studying the behaviour of the nodes under the various biaxial load combinations. In each case, relationships between the biaxial yield load, uniaxial yield load, diameter of node, thickness of node and material yield of node have been obtained using the method of least squares. The nodes have been analyzed under some selected Multi-axial loading and combinations of load which cause yield based on the second method proposed in Chapter 3 have been obtained and tabulated. However, a proper and thorough study of the nodes under multi-axial loading proved to be beyond the scope of this thesis. Chapter 5 contains the contributions made towards developing new methods and algorithms for obtaining the several results of chapters 2, 3 and 4, using object oriented programming (OOP) techniques. The contributions have been in Object Pascal, the underlying language of Delphi, a popular RAD tool developed by Borland/Inprise of USA. Several new modules have been developed to reliably handle the large amounts of data generated by the hundreds of analyses detailed in chapters 2,3 and 4. The ease with which new methods were possible to be incorporated into existing software using OOP has been demonstrated, with source code examples. Comparisons with other types of tools available and die advantages of using OOP have also been demonstrated using the experience during the preparation of this thesis. A strong case for OOP as an indispensable tool for the researcher has been made. Chapter 6: Several important conclusions and suggestions for future work have been made. Appendix 1 contains a brief note on the Method of Least Squares. Appendix 2 contains a small write-up on Delphi and OOP. Concepts of OOP have been briefly described and comparisons between three popular OOP languages have been attempted. A brief description of the features in Delphi's Object Pascal has also been provided. Appendix 3 contains the listing of Unit Arrays, which is a general purpose unit developed to make handling of large arrays easy. Several matrix calculations have been implemented which make the unit extremely useful for programmers. Appendix 4 contains the full listing of program FormK, which has been developed for chapter 2 to derive the fall stiffness matrix of a space frame node. The program picks up results from several analyses, forms a few columns of the stiffness matrix and then fills up the rest using the cyclic symmetry present in the space frame node. This program is given in full, with the intention that other researchers may find it useful to use it as-is or use after making small alterations to suit their circumstances. OOP is known for fast, reliable and easy ways of implementing modifications to existing code. Appendix 5 provides the full listing of the Object Pascal program for extracting Eigenvalues of a space truss with rigid joints or flexible joints. The incorporation of flexibility of the joints proposed in chapter 2 has been implemented. Descriptions of the program's implementations have been provided in chapter 5. Bibliography contains the alphabetical list of references.

The Formula SAE is a student based competition organised by SAE International where engineering students from a university design, develop and test a formula-style race car prototype to compete against other universities. The competition car needs to satisfy the competition rules set out by the organisers. The competition strives to stimulate original, creative problem solving together with innovative engineering design practices. In any race environment, the primary goal is always to be as competitive as possible. Due to the competitive nature of motor sport, vehicle components need to withstand various and severe stresses. The components of a race car vehicle are responsible for the vehicle’s handling characteristics and reliability. The chassis is a crucial and integral component of a Formula SAE competition car, primarily responsible for the vehicle’s performance characteristics. The chassis is the structural component that accommodates all the other components. A Formula SAE chassis is a structure that requires high torsional stiffness, low weight as well as the necessary strength properties. In this study, multiple Formula SAE chassis were designed and developed using computer aided design software. Each concept’s torsional stiffness, weight and strength properties were tested using finite element analysis software. The different concepts consisted of different design techniques and applications. All the concepts were analysed and assessed, leading to the identification of an acceptable prototype. The prototype was manufactured for experimental tests. The designed chassis complied with the Formula SAE rules and regulations. The weight, torsional stiffness and strength characteristics of the designed chassis frame were also favourable compared to accepted standards for Formula SAE chassis frames. The manufactured chassis was prepared for experimental tests in order to validate the simulation results produced by the finite element analysis. The torsional stiffness, weight and strength were experimentally determined and the results were compared with the corresponding simulations results. The comparison of the experimental and simulated results enabled the validation of the finite element analysis software. The study draws conclusions about the use of computer aided design and finite element analysis software as a design tool for the development of a Formula SAE chassis. Closure about the study is provided with general conclusions, recommendations and research possibilities for future studies. / MIng (Mechanical Engineering), North-West University, Potchefstroom Campus, 2014

The Formula SAE is a student based competition organised by SAE International where engineering students from a university design, develop and test a formula-style race car prototype to compete against other universities. The competition car needs to satisfy the competition rules set out by the organisers. The competition strives to stimulate original, creative problem solving together with innovative engineering design practices. In any race environment, the primary goal is always to be as competitive as possible. Due to the competitive nature of motor sport, vehicle components need to withstand various and severe stresses. The components of a race car vehicle are responsible for the vehicle’s handling characteristics and reliability. The chassis is a crucial and integral component of a Formula SAE competition car, primarily responsible for the vehicle’s performance characteristics. The chassis is the structural component that accommodates all the other components. A Formula SAE chassis is a structure that requires high torsional stiffness, low weight as well as the necessary strength properties. In this study, multiple Formula SAE chassis were designed and developed using computer aided design software. Each concept’s torsional stiffness, weight and strength properties were tested using finite element analysis software. The different concepts consisted of different design techniques and applications. All the concepts were analysed and assessed, leading to the identification of an acceptable prototype. The prototype was manufactured for experimental tests. The designed chassis complied with the Formula SAE rules and regulations. The weight, torsional stiffness and strength characteristics of the designed chassis frame were also favourable compared to accepted standards for Formula SAE chassis frames. The manufactured chassis was prepared for experimental tests in order to validate the simulation results produced by the finite element analysis. The torsional stiffness, weight and strength were experimentally determined and the results were compared with the corresponding simulations results. The comparison of the experimental and simulated results enabled the validation of the finite element analysis software. The study draws conclusions about the use of computer aided design and finite element analysis software as a design tool for the development of a Formula SAE chassis. Closure about the study is provided with general conclusions, recommendations and research possibilities for future studies. / MIng (Mechanical Engineering), North-West University, Potchefstroom Campus, 2014