Dissertations / Theses on the topic 'Lateral loads Mathematical models'

The loads applied to pile foundations installed offshore vary greatly from those encountered onshore, with more substantial lateral and torsional loads. For combined axial and lateral loading the current design practice involves applying an axial load to a deep foundation and assessing the pile behaviour and then considering a lateral load separately. For the problem of an altering directions of lateral loads (e.g. due to changes in the wind directions acting on offshore wind turbines) a clear design procedure is not available. There is thus a need for a clearly established methodology to effectively introduce the interaction between the four different loading directions (two lateral, one axial and one torsional). In this thesis, a model is presented that introduces a series of Winkler elasto-plastic elements coupled between the different directions via local interaction yield surfaces along the pile. The energy based method that is used allows the soil-pile system to be defined explicitly using two equations: the energy potential and the dissipation potential. One of the most interesting applications of this model is to piles subjected to a change in lateral loading direction, where the loading history can significantly influence the pile behaviour. This effect was verified by a series of experimental tests, undertaken using the Geotechnical Centrifuge at UWA. The same theory was then applied to cyclic loading in two dimensions, leading to some very useful conclusions regarding shakedown behaviour. A theoretically based relationship was applied to the local yielding behaviour for a pile subjected to a combination of lateral and axial loading, allowing predictions to be made of the influence of load inclination on the pile behaviour. The ability of this model to represent interaction between four degrees of freedom allows a more realistic approach to be taken to this problem than that considered in current design practice.

This dissertation focuses on improvements in vehicle routing that can be gained by allowing multiple vehicles to service a common load. We explore how costs can be reduced through the elimination of the constraint that a load must be serviced by only one vehicle. Specifically, we look at the problem of routing vehicles to service loads that have distinct origins and destinations, with no constraint on the amount of a load that a vehicle may service. We call this the Pickup and Delivery Problem with Split Loads (PDPSL). We model this problem as a dynamic program and introduce structural results that can help practitioners implement the use of split loads, including the definition of an upper bound on the benefit of split loads. This bound indicates that the routing cost can be reduced by at most one half when split loads are allowed. Furthermore, the most benefit occurs when load sizes are just above one half of vehicle capacity. We develop a heuristic for the solution of large scale problems, and apply this heuristic to randomly generated data sets. Various load sizes are tested, with the experimental results supporting the finding that most benefit with split loads occurs for load sizes just above one half vehicle capacity. Also, the average benefit of split loads is found to range from 6 to 7% for most data sets. The heuristic was also tested on a real world example from the trucking industry. These tests reveal the benefit of both using split loads and allowing fleet sharing. The benefit for split loads is not as significant as with the random data, and the various business rules added for this case are tested to find those that have the most impact. It is found that an additional cost for every stop the vehicle makes strictly limits the potential for benefit from split loads. Finally, we present a simplified version of the PDPSL in which all origins are visited prior to any destination on a route, generalizing structural results from the Split Delivery Vehicle Routing Problem for this problem.

Accurately predicting the response of complex bridge structures to strong earthquake ground motion requires the use of sophisticated nonlinear dynamic analysis computer programs not generally available to the bridge design engineer. The analytical tools that have been developed are generally applicable to bridges whose substructures can be idealized as beam-columns. Bridges with wall piers do not belong to this category The major objective of this study is to develop an analysis tool capable of simulating the effects of earthquakes on monolithic concrete wall pier bridges. Thus, after surveying the literature, a mathematical model is developed for the geometrically nonlinear earthquake analysis of wall pier bridges. Mixed plate elements are used to model the wall pier. The plate element has eight nodes and the degrees of freedom per node are three displacements and three moments. Beam elements are used to model the bridge deck. The beam element accounts for shear deformation and it has two nodes with three displacements and three rotations as degrees of freedom per node. A transitional element is used to join the beam elements to the plate elements. The equation of dynamic equilibrium is solved using the Newmark method with modified Newton-Raphson type iteration at each time step. The mixed plate element is used to model two plate structures and the results are compared with analytical and other finite element solutions. A two span wall pier bridge is modeled using the structural elements developed in this study. The digitized time history for the N-S component of the El Centro Earthquake of May 18, 1940, is used to seismically excite the bridge model.
Ph. D.

The objective of this research is to introduce a neural network based solution for the problem of measuring the actual amount of harmonic current injected into a power network by an individual nonlinear load. Harmonic currents from nonlinear loads propagate through the system and cause harmonic pollution. As a result, voltage at the point of common coupling (PCC) is rarely sinusoidal. The IEEE 519 harmonic standard provides customer and utility harmonic limits and many utilities are now requiring their customers to comply with IEEE 519. Measurements of the customer’s current at the PCC are expected to determine the customer’s compliance with IEEE 519. However, results in this research show that the current measurements at the PCC are not always reliable in that determination. In such a case, it may be necessary to determine what the customer’s true current harmonic distortions would be if the PCC voltage could be a pure sinusoidal voltage. However, establishing a pure sinusoidal voltage at the PCC may not be feasible since that would mean performing utility switching to reduce the system impedance. An alternative approach is to use a neural network that is able to learn the customer’s load admittance. Then, it is possible to predict the customer’s true current harmonic distortions based on mathematically applying a pure sinusoidal voltage to the learned load admittance. The proposed method is called load modeling. Load modeling predicts the true harmonic current that can be attributed to a customer regardless of whether a resonant condition exists on the utility power system. If a corrective action is taken by the customer, another important parameter of interest is the change in the voltage distortion level at the PCC due to the corrective action of the customer. This issue is also addressed by using the dual of the load modeling method. Topologies of the neural networks used in this research include multilayer perceptron neural networks and recurrent neural networks. The theory and implementation of a new neural network topology known as an Echo State Networks is also introduced. The proposed methods are verified on a number of different power electronic test circuits as well as field data. The main advantages of the proposed methods are that only waveforms of voltages and currents are required for their operation and they are applicable to both single and three phase systems. The proposed methods can be integrated into any existing power quality instrument or can be fabricated into a commercial standalone instrument that could be installed in substations of large customer loads, or used as a hand-held clip on instrument.

Thesis (MBA)--Stellenbosch University, 2008.
ENGLISH ABSTRACT: Auto Carrier Transport (ACT) is the motor ferrying division of Grindrod South Africa (Pty) Ltd and is contracted to transport the product of 15 different vehicle manufacturers. The division is responsible for ensuring that the combined annual volumes of each contract, totalling over 300 000 vehicles per year, are delivered to the right place, at the right time, and in the right condition. ACT's operating mandate thus focuses on the outbound logistics of new vehicles, which implies moving cars from either the local manufacturing plants, or from the import facilities at the ports, to the respective dealer networks all across Southern Africa. One of the key operational processes regarding the transportation of vehicles is the allocation of cars to carrier loads, also known as load building. Once cars have been allocated to a load, a carrier is then used to transport the load. The existing load building operation is completely manual, with operators simply assigning cars to loads as best they see fit. No support systems exist. Thus, given the complexity of the load building problem, and the manual processes used, existing load building practices result in suboptimal payload performances. A Linear Programming Model was developed to improve the manner in which vehicles are categorised, and then assigned to loads. When compared against the results of load building operators, it was found that the model could potentially improve the company's contribution margin by 5.8 percent.
AFRIKAANSE OPSOMMING: Auto Carrier Transport (ACT) is die motorvoertuig vervoerafdeling van Grindrod Suid Afrika (Edms) Bpk en word gekontrakteer vir die vervoer van die produkte van 15 verskillende motorvervaardigers. Die afdeling is verantwoorde1ik om te verseker dat die jaarlikse volume van elke kontrak (met 'n gekombineerde volume van meer as 300 000 motorvoertuie per jaar) betyds afgelewer word, op die regte plek en in die regte toestand. ACT se operasionele mandaat fokus dus op die uitgaande logistiek van nuwe motorvoertuie met die implikasie dat motorvoertuie vanaf die plaaslike vervaardingsaanleg, of die invoer fasiliteit by die hawens, na die ooreenstemende handelaarsnetwerke in Suider Afrika vervoer word. Een van die kern operasionele prosesse rakende die vervoer van motorvoertuie, wat bekendstaan as vragtoekening, is die toedeling van motorvoertuie tot vragmotor vragte. Sodra 'n motorvoertuig aan 'n vrag toegeken is, word dit deur middel van 'n vragmotor vervoer. Die bestaande vragtoekeningsproses word per hand uitgevoer deur operateurs wat eenvoudig motorvoertuie aan vragte toedeel soos hulle goeddink sonder die gebruik van enige besluitnemingsondersteuningstelsels. Aangesien vragtoekening 'n baie komplekse probleem is wat per hand uitgevoer word, is die resultate suboptimaal. 'n Lineêre programeeringsmodel is ontwikkel om die klassifikasie van motorvoertuie te verbeter waarna die motorvoertuie aan vragte toegeken word. In 'n vergelyking tussen die model se resultate en die van die operateurs is daar bevind dat die model die maatskappy se wins per eenheid met 5.8 persent kan verbeter.

This research work proposes methods to rises the resistance and to evaluate the behavior of confined masonry walls built from clay solid bricks. These elements are widely used in Guerrero State (México) to build masonry structures, which should resist high lateral loads because of the serious seismic hazard. Therefore, a large experimental program to evaluate the mechanical properties of bricks and masonry currently required in the design process and masonry analysis was developed. To rises the masonry resistance and to counteract the influence of the compressive strength of the pieces on the masonry behavior, a high compressive strength mortar and a metallic reinforcement inside the joints were used. With respect to referenced values of the mechanical properties, some were similar and others were twice bigger. In this country zone, the first three tests under lateral load on full-scale confined masonry walls built from clay solid bricks were carried out in order to evaluate its behavior. A reinforcement composed by metallic hexagonal mesh-mortar coat was placed on the faces of two walls to rise or to restore the resistance. The walls showed good behavior and the reinforcement had adequate structural efficiency. Numerical models of panels and walls built by using the experimental data evaluated the envelope resistance, the failure mode and showed the influence of the mechanical properties of the pieces and joints on the global behavior. Two models had metallic reinforcement inside the joints. In addition, a constitutive law of the masonry defined from experimental results allowed to elaborate a simple model, which results were concordant with respect to the experimental results and similar to those calculated by complex models. Finally, two simplified models to evaluate the resistance of confined masonry walls by considering the failure plane on the wall diagonal were developed. One supposes the masonry failure by shear effect and the other supposes the masonry failure by induced tension. The ratio theoretical resistance vs. experimental resistance was adequate for walls built from different materials and tested under different loads, which had ratio Height/Length ranging from 0.74 to 1.26

[Truncated abstract] The hydrodynamics of wave impact on offshore structures is not well understood. Wave impacts often involve large deformations of water free-surface. Therefore, a wave impact problem is usually combined with a free-surface problem. The complexity is expanded when the body exposed to a wave impact is allowed to move. The nonlinear interactions between a moving body and fluid is a complicated process that has been a dilemma in the engineering design of offshore and coastal structures for a long time. This thesis used experimental and numerical means to develop further understanding of the wave impact problems as well as to create a numerical tool suitable for simulation of such problems. The study included the consideration of moving boundaries in order to include the coupled interactions of the body and fluid. The thesis is organized into two experimental and numerical parts. There is a lack of benchmarking experimental data for studying fluid-structure interactions with moving boundaries. In the experimental part of this research, novel experiments were, therefore, designed and performed that were useful for validation of the numerical developments. By considering a dynamical system with only one degree of freedom, the complexity of the experiments performed was minimal. The setup included a plate that was attached to the bottom of a flume via a hinge and tethered by two springs from the top one at each side. The experiments modelled fluid-structure interactions in three subsets. The first subset studied a highly nonlinear decay test, which resembled a harsh wave impact (or slam) incident. The second subset included waves overtopping on the vertically restrained plate. In the third subset, the plate was free to oscillate and was excited by the same waves. The wave overtopping the plate resembled the physics of the green water on fixed and moving structures. An analytical solution based on linear potential theory was provided for comparison with experimental results. ... In simulation of the nonlinear decay test, the SPH results captured the frequency variation in plate oscillations, which indicated that the radiation forces (added mass and damping forces) were calculated satisfactorily. In simulation of the nonlinear waves, the waves progressed in the flume similar to the physical experiments and the total energy of the system was conserved with an error of 0.025% of the total initial energy. The wave-plate interactions were successfully modelled by SPH. The simulations included wave run-up and shipping of water for fixed and oscillating plate cases. The effects of the plate oscillations on the flow regime are also discussed in detail. The combination of experimental and numerical investigation provided further understanding of wave impact problems. The novel design of the experiments extended the study to moving boundaries in small scale. The use of SPH eliminated the difficulties of dealing with free-surface problems so that the focus of study could be placed on the impact forces on fixed and moving bodies.

Development of variable speed horizontal axis wind turbines has resulted in a need for an analysis code with a rotor speed degree-of-freedom. This study develops a five degree-of-freedom time domain computer code that evaluates blade and rotor, mean and cyclic loads with nonlinear aerodynamics together with atmospheric turbulence as a forcing function. Verification of the model is made by comparison of loads predictions between ESI-80 wind turbine data and analytical solutions. Results show good agreement for mean and cyclic loads and teeter angle excursions. A single-blade point turbulence simulation model is optimized using a three-blade point turbulence simulation model. The optimum point is the 80% radius location, although a multiplying factor is needed to make conservative fatigue cycle predictions of blade bending. ESI-80 start-up and shutdown scenarios are examined, prediction trends matched ESI-80 data. Three generator models are investigated. Results show that generator torque cycles are reduced and yearly energy capture increased by 24% when a variable speed generator is implemented.
Graduation date: 1991

This thesis presents a theoretical study into the behaviour of thin-walled metal tubes that are filled with elastic material. The study has considered the behaviour and design of concrete-filled steel columns by analysing the effect of the combined actions of axial compression and bending on closed stainless steel cross-sections with a concrete infill as well as the elastic buckling of square, circular and elliptical thin-walled steel tubes, when filled with elastic material. The elastic local buckling of a rectangular plate having four edges clamped and subjected to in-plane linearly varying uniaxial loading with and without juxtaposition with a rigid infill has also been studied. Concrete-filled composite columns find widespread use globally in engineering structures because of their optimal strength and ease of construction. Enhancing the strength of filled columns by utilising newer materials such as stainless steel or shape memory alloys for the skin of the cross-section of the column will increase the construction cost of the column. In order to circumvent this increased construction cost, or to minimise it, the metal skin should be as thin as possible. Members with thin-walled cross-section are prone to lateral torsional buckling, and in particular they are prone to local buckling, with the latter buckling mode playing an important role in the strength of a composite column with a concrete infill. The local buckling coefficient is enhanced by the provision of a rigid concrete infill, and efficient design must make use of this fact to minimise the cost of the skin. The initial portions of this thesis demonstrate the beneficial effects that the rigid concrete core has on the overall strength, and also on the local buckling behaviour of thin-walled metal tubes. The local buckling of the metal skin has been modelled in this thesis by using a Ritz-based energy method. In bi-lateral and uni-lateral buckling studies of rectangular plates, a more general trigonometric function has been selected by application of boundary conditions to the chosen shape function, with these boundary conditions being implemented to make the chosen shape function satisfy the edge conditions for the problem under consideration. The restraining medium is modelled as a tensionless foundation and this restraint condition is introduced through a penalty method formulation. Extensive comparative, convergence, and parametric studies have been carried out by considering a wide range of uni-laterally constrained plates. Following a concise review of the available literature, techniques for analysing the elastic local buckling of thin-walled square tubes, fully filled with elastic materials and subjected to concentric uni-axial compression, are formulated by means of a simple stiffness approach and a proper Ritz-based technique. This method is then extended to account for the local buckling of thin-walled circular and elliptical cylinders with elastic infill. By representation of a proper trigonometric displacement function in the formulation which is capable of incorporating the effects of the penetration zone in a harmonic form, in addition to satisfying all the necessary boundary conditions, it is shown that the buckling solution reduces to a dimensionless representation for which the relevant geometrical and material properties that govern the local buckling coefficient can be identified. It was found that the provision of lightweight and low density infill is functional and attractive with respect to an increase in the efficacy of the restraint. A comparison was made, and good agreement was found to exist, between the results obtained from this study and results that are available in the literature. Finally, a strength to weight index is introduced that quantifies the enhancement in the local buckling coefficient for a number of materials with a wide range of stiffness and density. This index has potential applications for optimal design in aerospace and other specialized engineering applications.

The objective of this study was to develop and validate practical modeling methods for investigating load paths and system behavior in a realistic, light-frame wood structure. The modeling methods were validated against full-scale tests on subassemblies and an L-shaped house. The model of the L-shaped house was then modified and used to investigate the effects of re-entrant corners, wall openings and gable-end retrofits on system behavior and load paths. Results from this study showed that the effects of adding re-entrant corners and wall openings on uplift load distributions were dependent on the orientation of the trusses with respect to the walls. Openings added to walls parallel to the trusses had the least effect on loads carried by the remaining walls in the building. Varying re-entrant corner dimensions of the L-shaped house under ASCE 7-05 (ASCE 2005) design wind loads caused increasing degrees of torsion throughout the house, depending on the relative location and stiffness of the in-plane walls (parallel to the applied wind loads) as well as the assumed direction of the wind loads. Balancing the stiffness of the walls on either side of the house with the largest re-entrant corner helped to decrease torsion in the structure somewhat. Finally, although previous full-scale tests on gable-end sections verified the effectiveness of the gable-end retrofit that was recently adopted into the 2010 Florida building code, questions remained about the effects of the retrofit on torsion in a full building. The current study found that adding the gable-end retrofits to the L-shaped house did not cause additional torsion.
Graduation date: 2013

"November 2004"
Bibliography: p.167-179.
xi, 333 p. : ill., photos (col.) ; 30 cm.
Title page, contents and abstract only. The complete thesis in print form is available from the University Library.
Focuses on behavioural models of masonry walls with a view to improving their accuracy and extending their application. Results include a numerical model and mathematical expressions capable of predicting the key stages of the non-linear load-deflection behaviour of walls subjected to vertical bending and axial loading; new mathematical expressions for horizontal and diagonal bending moment capacities that are dimensionally consistent and account for the beneficial effects of compressive stress; and. Experimental test data for masonry sections subjected to horizontal and diagonal bending, which were used in the development and verification of the new mathematical expressions.
Thesis (Ph.D.)--University of Adelaide, School of Civil and Environmental Engineering, 2004

The effects of thermal loads on steel bridges are not well understood. Although thermal effects are discussed in the AASHTO specifications, the appropriateness of the recommended thermal gradients is questionable. Thermal effects on the bridges can impact the design of the steel superstructure, the support bearings, and even the bridge piers. Previous field monitoring of steel trapezoidal box girder bridges has shown that thermal stresses on the order of ±5 ksi were not uncommon under regular daily thermal cycles. Stresses induced during annual thermal cycles may be potentially larger than those during daily thermal cycles. Recent data has shown that the bearings that are to allow the girders to expand and contract freely due to thermal movements are not frictionless. Because of the bearing friction, the supporting piers must flex to accommodate the bridge movements. In curved girder applications, questions have been raised by designers and contractors regarding the proper orientation of guided bearings. This research study includes field measurements, laboratory tests and finite element parametric analyses. The bearings of nine bridges in the Houston area have been instrumented and monitored for more than a year to measure bearing movements due to changes in temperature. Instrumentation of the steel girders on one of the Houston bridges was made utilizing thermocouples and vibrating wire strain gages to measure temperature distribution and thermal stresses. In addition, strain gages and thermal couples were applied to the steel girders and concrete bridge deck on a simple twin box girder bridge located at the Ferguson Structural Engineering Laboratory in Austin, Texas. The data from the field monitoring and laboratory tests were used to validate a finite element model. Based on this model, a detailed parametric study was conducted to investigate the effects of bridge configuration. It is found that under the given weather conditions, the most critical thermal loads are achieved under the following bridge configurations: N-S bridge orientation, shorter lengths of the concrete deck overhang, deeper steel girder webs, thinner concrete decks, and larger spacing between two box girders. To evaluate the effect of environmental conditions and obtain extreme thermal loads for design purposes, the most critical configuration of bridge sections was modeled for thermal analysis with Texas weather data from 1961 to 2005 as the input environmental conditions. Four cities were considered to bound Texas weather conditions. Based on the thermal analyses, a 45-year sample data of thermal parameters were used to describe the temperature field over a section. Extreme value analyses of the sample data were performed to obtain the relationship between thermal loads and return periods. The thermal loads with 100-year return period were compared to the ones suggested by AASHTO. The thermal loads with 100-year return period were used to investigate structural response. The effect of bearing orientation and the point of fixity were studied. A rigid body model was proposed to estimate thermal movements at the ends, which matched those obtained from field monitoring and finite element analysis. The maximum possible thermal stresses were also evaluated. Design suggestions are put forward based on the analysis.
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Stability is an important criterion in the design and performance of launch vehicles. Present day launch vehicles have become more and more flexible due to the constraints of weight reduction, necessarily imposed for enhanced performance of the vehicle. Due to higher flexibility, the launch vehicle stability becomes a concern. Instability in the launch vehicles has been noticed due to three major sources: thrust, aerodynamic forces and combustion induced instabilities. Instability in the launch vehicles may pose problem to the structural integrity leading to structural failure or it may lead to the deviation in the trajectory of the vehicle. Several structural failures of launch vehicles due to instabilities have been reported in the literature. The prediction of the structural response due to various excitations such as thrust and aerodynamic loading is essential to identify any failure scenarios and to limit the vibrations transmitted to the payload. Therefore, determination of dynamic and stability characteristics of a launch vehicle under the influence of different parameters, is of vital importance. Disciplines such as, flight mechanics (dynamics), structural dynamics, aerodynamics, propulsion, guidance and control are closely related in the design and analysis of launch vehicles. Typically, flight mechanics, guidance and control problems consider a rigid vehicle for modeling and simulation purposes. The disciplines of structural dynamics and aeroelasticity consider a flexible vehicle. In order to bring in the effect of flexibility on the flight dynamics of the launch vehicle, structural dynamics and aeroelasticity aspects need to be effected. The preliminary design of a new launch vehicle requires inputs from different disciplines and parametric studies are required to finalise the vehicle configuration. The study of the effect of different parameters on the dynamics and stability of launch vehicles is required. In this context, there is a need to develop an integrated approach that provides tools for the design and analysis of a launch vehicle. The availability of integrated modeling and simulation tools will reduce the requirement of costly prototype development and testing. In the present thesis, an attempt has been made to develop a numerical tool to conduct parametric studies for launch vehicle dynamics and stability. The developed tool is suitable for prediction of onset of instabilities under the influence of different parameters. The approach developed in this thesis is also well suited for specialized analysis of problems involving vertical launch, stage separation, engine shutdown and internal stress wave propagation related to structural integrity. Stability problems due to thrust and the aerodynamic forces (aeroelastic stability) in the launch vehicles/ missiles have been reported in the literature. Most of these works have modeled the vehicle as a beam or by using discrete degrees of freedom. In these works, the effect of thrust or aerodynamic forces on the flexible body modes is investigated and it is shown that the instability may occur in one of the bending modes due to change in the parameters such as thrust or aerodynamic forces. Traditionally, the dynamic characteristics are obtained in a body-fixed coordinate system, whereas the prediction of trajectory (rigid body dynamics) is carried out in an inertial frame of reference. Only few works have addressed the coupling of the rigid body motion and the flexible body dynamics of a vehicle. But these works also, do not consider the total derivative of displacements with respect to an inertial frame of reference. When the integrated equations of motion are derived in an inertial frame of reference, the rigid body motion and the elastic displacements are highly coupled. In this thesis, the rigid body motion and the flexible body dynamics is studied in an inertial frame of reference. The flexible body dynamics of the moving vehicle is studied in an inertial frame of reference, including velocity induced curvature effects, which have not been considered so far in the published literature. A detailed mechanics based model is developed to analyze the problem of structural instabilities in launch vehicles. Coupling among the rigid-body modes, the longitudinal vibrational modes and the transverse vibrational modes due to asymmetric lifting-body cross-section are considered. The model also incorporates the effects of aerodynamic forces and the propulsive thrust of the vehicle. The propulsive thrust is considered as a follower force. The model is one-dimensional, and it can be employed to idealized slender vehicles with complex shapes. The governing differential equations along with the boundary conditions are derived using Extended Hamilton’s principle. Subsequently, the modeling of the propulsive thrust and the aerodynamic forces are included in the formulation. In the literature, the propulsive thrust has generally been modeled as a follower force applied at the nozzle end. Few of the works in the literature have modeled the combustion process in the solid rocket motor and the liquid propellant engine in detail. This is required to understand the combustion induced instabilities. In the present thesis, the propulsive thrust is considered as a follower force and few of the combustion parameters affecting the thrust are considered. In the literature, the modeling of the aerodynamic forces acting on a launch vehicle has been carried out using general purpose computational fluid dynamics (CFD) codes or by using empirical methods. CFD codes are used to obtain the pressure and the shear stress distribution on the vehicle surface by the solution of Navier Stokes/ Euler equations. The empirical methods have been used to obtain the distributed aerodynamic forces acting on the vehicle. The aerodynamic forces are expressed in terms of distributed aerodynamic coefficients. In the present work, the modeling of the aerodynamic forces has been carried out in two different ways: using a CFD package and by using empirical methods. The stability of a system can be studied by determining the system response with time. Eigenvalue analysis is another tool to investigate the stability of a linear system. To study the stability characteristics of the system using eigenvalue analysis, a computational framework has been developed. For this purpose, the finite element discretization of the system is carried out. Further to that, two different methods are utilized for finite element discretization of the vehicle structure: Fourier Transform based Spectral Finite Element method (SFEM) and an hp Finite Element method (FEM). The conventional FEM is a versatile tool for modeling complicated structures and to obtain the solution of the system of equations for a variety of forcing functions. The SFEM is more suitable for obtaining the solution for simple 1D and 2D structures subjected to shock and transient loads, having high frequency content. In this thesis, the spectral finite element model is developed for a vehicle subjected to the propulsive thrust and the aerodynamic forces. Prediction of instability using SFEM, means solving a nonlinear eigenvalue problem. Standard computer codes or routines are not available for solving a nonlinear eigenvalue problem. A computer code has been written to solve the nonlinear eigenvalue problem using one of the algorithms available in the literature. An hp finite element model is also developed for launch vehicle. The finite element stiffness and damping matrices due to the thrust, the aerodynamic forces and the rigid body velocity and acceleration are derived using Lagrange’s equations of motion. A standard linear eigenvalue problem and a polynomial eigenvalue problem is formulated for determination of instability regimes of the vehicle. It is important to understand the influence of different parameters such as thrust, velocity, angle of attack etc. on the stability of a launch vehicle. Parametric studies are important during the preliminary design phase of a vehicle to identify the instability regimes. The design parameters can be changed to reduce the possibility of instabilities. Numerical simulations are carried out to determine the unstable regimes of a slender launch vehicle for propulsive thrust and velocity as the parameters, neglecting the aerodynamic forces. Comparison between the results based on a Fourier spectral finite element model and a hp finite element model are carried out. Phenomenon of static instability (divergence) and dynamic instability (flutter) are observed. Determination of mode shapes of the vehicle is important for deciding the placement of sensors and actuators on the vehicle. In this context, eigenvectors (mode shapes) for different end thrust and speed are analyzed. Further, numerical simulations are also carried out to determine the instabilities in a slender launch vehicle considering the combined effects of propulsive thrust, aerodynamic forces and mass variation. The finite element model simulation results for aeroelastic effects are compared with the published literature. Stability of a vehicle is analysed for velocity (free stream Mach number) as a parameter, at maximum propulsive thrust, including the effect of aerodynamic forces and mass variation. Phenomenon of static instability (divergence) and dynamic instability (flutter) are observed. With the increase in the Mach number, branching (splitting) and merging of the modes is observed. At higher Mach numbers, divergence and flutter are observed in different modes simultaneously. Numerical simulations are carried out for a typical nosecone launch vehicle configuration to analyse the aeroelastic stability at two different Mach numbers using empirical aerodynamic data. The phenomenon of flow separation and reattachment is observed at the cone-cylinder junction. The stability of a typical vehicle under propulsive thrust and aerodynamic forces is investigated using CFD derived aerodynamic data. The aerodynamic pressure and shear stress distribution for a launch vehicle are obtained from the CFD analysis. The effect of different parameters such as combustion chamber pressure, tip mass and slenderness ratio on the stability of a vehicle is studied. In the later part of the thesis, solution methodology for the time domain response for a coupled axial and transverse motion of a vehicle is developed. The axial responses (displacements and velocities) of a typical vehicle subjected to axial thrust are determined using direct integration of the equations of motion. The axial displacements due to two different thrust histories are compared. The axial velocities with time at different locations are determined. The time domain and the frequency domain responses for a representative vehicle subjected to a transverse shock force are determined using Spectral Finite Element method (SFEM). The system of equations for a coupled axial and transverse motion of a vehicle is developed. Numerical simulations are carried out to determine the coupled axial and transverse response of a vehicle subjected to axial and transverse forces. The coupling of rigid body motion with the elastic displacements is illustrated. The thesis is comprised of seven chapters. The first chapter gives a detailed introduction to launch vehicles and covers literature survey of launch vehicle dynamics and stability. The dynamics and stability related aspects of flexible structures are also discussed. In chapter 2, a detailed mathematical model of a slender launch vehicle is developed to analyze the problem of structural instabilities. Chapter 3 deals with the finite element discretization of the vehicle structure using two different methods: Fourier spectral finite element method and an hp finite element method. In chapters 4 and 5, numerical simulations are carried out to determine the instabilities in a slender launch vehicle considering the effects of propulsive thrust, aerodynamic forces and mass variation. In chapter 6, solution methodology for the time domain response for a coupled axial and transverse motion of a vehicle is developed. The last chapter gives the conclusions and the future scope of work. To summarize, this thesis is a comprehensive document, that not only describes some detailed mathematical models for launch vehicle stability studies, but also presents the effect of aerodynamic, propulsion and structural loads on the launch vehicle stability. Linear stability analysis of a representative vehicle is carried out for prediction of onset of the instabilities under the influence of different parameters such as velocity, thrust, combustion factors etc. The correlation between the stability analysis and the time domain response is established. In short, the matter presented in this thesis can serve as a useful design aide for those working in the launch vehicle design.