The conventional finite element models (FEM) of problems in structural mechanics are based on the principles of virtual work and the total potential energy. In these models, the secondary variables, such as the bending moment and shear force, are post-computed and do not yield good accuracy. In addition, in the case of the Timoshenko beam theory, the element with lower-order equal interpolation of the variables suffers from shear locking. In both Euler-Bernoulli and Timoshenko beam theories, the elements based on weak form Galerkin formulation also suffer from membrane locking when applied to geometrically nonlinear problems. In order to alleviate these types of locking, often reduced integration techniques are employed. However, this technique has other disadvantages, such as hour-glass modes or spurious rigid body modes. Hence, it is desirable to develop alternative finite element models that overcome the locking problems. Least-squares finite element models are considered to be better alternatives to the weak form Galerkin finite element models and, therefore, are in this study for investigation. The basic idea behind the least-squares finite element model is to compute the residuals due to the approximation of the variables of each equation being modeled, construct integral statement of the sum of the squares of the residuals (called least-squares functional), and minimize the integral with respect to the unknown parameters (i.e., nodal values) of the approximations. The least-squares formulation helps to retain the generalized displacements and forces (or stress resultants) as independent variables, and also allows the use of equal order interpolation functions for all variables. In this thesis comparison is made between the solution accuracy of finite element models of the Euler-Bernoulli and Timoshenko beam theories based on two different least-square models with the conventional weak form Galerkin finite element models. The developed models were applied to beam problems with different boundary conditions. The solutions obtained by the least-squares finite element models found to be very accurate for generalized displacements and forces when compared with the exact solutions, and they are more accurate in predicting the forces when compared to the conventional finite element models.

Adhesively bonded joints have been investigated for several decades. In most analytical studies, the Bernoulli-Euler beam theory is employed to describe the behaviour of adherends. In the current work, three analytical models are developed for adhesively bonded joints using the Timoshenko beam theory for elastic material and a Bernoulli-Euler beam model for viscoelastic materials. One model is for the peeling test of an adhesively bonded joint, which is described using a Timoshenko beam on an elastic foundation. The adherend is considered as a Timoshenko beam, while the adhesive is taken to be a linearly elastic foundation. Three cases are considered: (1) only the normal stress is acting (mode I); (2) only the transverse shear stress is present (mode II); and (3) the normal and shear stresses co-exist (mode III) in the adhesive. The governing equations are derived in terms of the displacement and rotational angle of the adherend in each case. Analytical solutions are obtained for the displacements, rotational angle, and stresses. Numerical results are presented to show the trends of the displacements and rotational angle changing with geometrical and loading conditions. In the second model, the peeling test of an adhesively bonded joint is represented using a viscoelastic Bernoulli-Euler beam on an elastic foundation. The adherend is considered as a viscoelastic Bernoulli-Euler beam, while the adhesive is taken to be a linearly elastic foundation. Two cases under different stress history are considered: (1) only the normal stress is acting (mode I); and (2) only the transverse shear stress is present (mode II). The governing equations are derived in terms of the displacements. Analytical solutions are obtained for the displacements. The numerical results show that the deflection increases as time and temperature increase. The third model is developed using a symmetric composite adhesively bonded joint. The constitutive and kinematic relations of the adherends are derived based on the Timoshenko beam theory, and the governing equations are obtained for the normal and shear stresses in the adhesive layer. The numerical results are presented to reveal the normal and shear stresses in the adhesive.

Research is performed to assess the viability of applying the least squares model to one-dimensional heat transfer and Euler-Bernoulli Beam Theory problems. Least squares models were developed for both the full and mixed forms of the governing one-dimensional heat transfer equation along weak form Galerkin models. Both least squares and weak form Galerkin models were developed for the first order and second order versions of the Euler-Bernoulli beams. Several numerical examples were presented for the heat transfer and Euler- Bernoulli beam theory. The examples for heat transfer included: a differential equation having the same form as the governing equation, heat transfer in a fin, heat transfer in a bar and axisymmetric heat transfer in a long cylinder. These problems were solved using both least squares models, and the full form weak form Galerkin model. With all four examples the weak form Galerkin model and the full form least squares model produced accurate results for the primary variables. To obtain accurate results with the mixed form least squares model it is necessary to use at least a quadratic polynominal. The least squares models with the appropriate approximation functions yielde more accurate results for the secondary variables than the weak form Galerkin. The examples presented for the beam problem include: a cantilever beam with linearly varying distributed load along the beam and a point load at the end, a simply supported beam with a point load in the middle, and a beam fixed on both ends with a distributed load varying cubically. The first two examples were solved using the least squares model based on the second order equation and a weak form Galerkin model based on the full form of the equation. The third problem was solved with the least squares model based on the second order equation. Both the least squares model and the Galerkin model calculated accurate results for the primary variables, while the least squares model was more accurate on the secondary variables. In general, the least-squares finite element models yield more acurate results for gradients of the solution than the traditional weak form Galkerkin finite element models. Extension of the present assessment to multi-dimensional problems and nonlinear provelms is awaiting attention.

This thesis attempts to shed light on the process approach developed at Prickly Mountain, Vermont by investigating the influence of Yale professors Robert Engman and Chris Argyris. As a sculptor, Professor Engman influenced the way in which Prickly Mountain builders interacted with their materials, allowing space for discovery. On the other hand, professor Argyris from the Industrial Administration program inspired Prickly Mountain builders to consider the element of human behavior in interacting with their structures. Argyris' teaching also inspired critical engagement with the practice of architectural education. Together, Engman and Argyris present a more in depth picture of the design process at Prickly Mountain and thus help to provide an academic footing for this otherwise eccentric practice.

No description available.

Nonlinear finite element models of functionally graded beams with power-law variation of material, accounting for the von-Karman geometric nonlinearity and temperature dependent material properties as well as microstructure dependent length scale have been developed using the Euler-Bernoulli as well as the first-order and third- order beam theories. To capture the size effect, a modified couple stress theory with one length scale parameter is used. Such theories play crucial role in predicting accurate deflections of micro- and nano-beam structures. A general third order beam theory for microstructure dependent beam has been developed for functionally graded beams for the first time using a modified couple stress theory with the von Karman nonlinear strain. Finite element models of the three beam theories have been developed. The thermo-mechanical coupling as well as the bending-stretching coupling play significant role in the deflection response. Numerical results are presented to show the effect of nonlinearity, power-law index, microstructural length scale, and boundary conditions on the bending response of beams under thermo-mechanical loads. In general, the effect of microstructural parameter is to stiffen the beam, while shear deformation has the effect of modeling more realistically as a flexible beam.

A principal característica de cabos é a sua capacidadede suportar grande carga na direção longitudinal e são utilizadas em, por exemplo, concreto comprimido, plataformas e pontes. Usualmente, sua estrutura básica é formada por um elemento central (núcleo) e reto juntamente com outros componentes dispostos ao seu redor em forma de hélice. Existe uma variedade de geometrias que podem ser utilizadas, assim como número de camadas. Seguindo a teoria de vigas espaciais e parametrizando a geometria, a linha média de apenas uma dessas hélices foi analisada analiticamente. Essa simplificação é valida visto que o contato e deslizamento não são incluídos nesta teoria, produzindo uma primeira abordagem ao problema da modelagem dessas estruturas. Sendo assim, as equações de equilíbrio foram deduzidas e seu sistema diferencial foi resolvido com o objetivo de representar o comportamento mecânico da estrutura. Utilizando a tríade de Frenet-Serret para definir um sistema de coordenadas local, as condições de contorno foram aplicadas buscando determinar as constantes de integração resultantes da solução analítica das equações diferenciais. Essa solução foi comparadas com resultados numéricos obtidos pelo Método dos Elementos Finitos (FEM) para validação dos casos de carga concentrada e distribuída em duas geometrias, o arco plano e a hélice. Em ambos os casos resultados apresentaram boa concordância para forças, momentos, rotações e deslocamentos. Considerando o caso do arco, o seu raio foi aumentado, de forma que a geometria se aproximasse de uma viga reta. O modelo proposto também foi utilizado para simular uma mola sob compressão. / A high number of structures uses cables due to their ability to bear large load in the longitudinal direction, for example, prestressed concrete, offshore systems and bridges. Its basic structure is formed by a central straight element surrounded by strands laid helically. A variety of geometries can be used, as well as the number of layers. Using the theory of spatial beams and parameterizing the geometry, the center line of only one of these helixes was analyzed analytically, since contact and slip are not included in this theory, obtaining a first approach in order to model these structures and to determine its mechanical behavior. Thus, the equilibrium equations were deduced and the differential system was solved with the objective of representing the mechanical behavior of the structure. Using the Frenet-Serret triad to define a local coordinate system, the boundary conditions were applied aiming the determination of the integration constants. The expressions obtained were compared with results obtained by the Finite Element Method (FEM) for validation applying concentrated and distributed loads. All cases presented good agreement FOR forces, moments, rotations and displacements. Considering the arc case, its radius was increased until a straight beam. The proposed model was also used to simulate a spring under compression.

Beams are structural members with one dimension much larger than the other two. Examples of beams include propeller blades, helicopter rotor blades, and high aspect-ratio aircraft wings in aerospace engineering; shafts and wind turbine blades in mechanical engineering; towers, highways and bridges in civil engineering; and DNA modeling in biomedical engineering. Beam analysis includes two sets of equations: a generally linear two-dimensional problem over the cross-sectional plane and a nonlinear, global one-dimensional analysis. This research work deals with a relatively new set of equations for one-dimensional beam analysis, namely the so-called fully intrinsic equations. Fully intrinsic equations comprise a set of geometrically exact, nonlinear, first-order partial differential equations that is suitable for analyzing initially curved and twisted anisotropic beams. A fully intrinsic formulation is devoid of displacement and rotation variables, making it especially attractive because of the absence of singularities, infinite-degree nonlinearities, and other undesirable features associated with finite rotation variables. In spite of the advantages of these equations, using them with certain boundary conditions presents significant challenges. This research work will take a broad look at these challenges of modeling various boundary conditions when using the fully intrinsic equations. Hopefully it will clear the path for wider and easier use of the fully intrinsic equations in future research. This work also includes application of fully intrinsic equations in structural analysis of joined-wing aircraft, different rotor blade configuration and LCO analysis of HALE aircraft.

A principal característica de cabos é a sua capacidadede suportar grande carga na direção longitudinal e são utilizadas em, por exemplo, concreto comprimido, plataformas e pontes. Usualmente, sua estrutura básica é formada por um elemento central (núcleo) e reto juntamente com outros componentes dispostos ao seu redor em forma de hélice. Existe uma variedade de geometrias que podem ser utilizadas, assim como número de camadas. Seguindo a teoria de vigas espaciais e parametrizando a geometria, a linha média de apenas uma dessas hélices foi analisada analiticamente. Essa simplificação é valida visto que o contato e deslizamento não são incluídos nesta teoria, produzindo uma primeira abordagem ao problema da modelagem dessas estruturas. Sendo assim, as equações de equilíbrio foram deduzidas e seu sistema diferencial foi resolvido com o objetivo de representar o comportamento mecânico da estrutura. Utilizando a tríade de Frenet-Serret para definir um sistema de coordenadas local, as condições de contorno foram aplicadas buscando determinar as constantes de integração resultantes da solução analítica das equações diferenciais. Essa solução foi comparadas com resultados numéricos obtidos pelo Método dos Elementos Finitos (FEM) para validação dos casos de carga concentrada e distribuída em duas geometrias, o arco plano e a hélice. Em ambos os casos resultados apresentaram boa concordância para forças, momentos, rotações e deslocamentos. Considerando o caso do arco, o seu raio foi aumentado, de forma que a geometria se aproximasse de uma viga reta. O modelo proposto também foi utilizado para simular uma mola sob compressão. / A high number of structures uses cables due to their ability to bear large load in the longitudinal direction, for example, prestressed concrete, offshore systems and bridges. Its basic structure is formed by a central straight element surrounded by strands laid helically. A variety of geometries can be used, as well as the number of layers. Using the theory of spatial beams and parameterizing the geometry, the center line of only one of these helixes was analyzed analytically, since contact and slip are not included in this theory, obtaining a first approach in order to model these structures and to determine its mechanical behavior. Thus, the equilibrium equations were deduced and the differential system was solved with the objective of representing the mechanical behavior of the structure. Using the Frenet-Serret triad to define a local coordinate system, the boundary conditions were applied aiming the determination of the integration constants. The expressions obtained were compared with results obtained by the Finite Element Method (FEM) for validation applying concentrated and distributed loads. All cases presented good agreement FOR forces, moments, rotations and displacements. Considering the arc case, its radius was increased until a straight beam. The proposed model was also used to simulate a spring under compression.

A principal característica de cabos é a sua capacidadede suportar grande carga na direção longitudinal e são utilizadas em, por exemplo, concreto comprimido, plataformas e pontes. Usualmente, sua estrutura básica é formada por um elemento central (núcleo) e reto juntamente com outros componentes dispostos ao seu redor em forma de hélice. Existe uma variedade de geometrias que podem ser utilizadas, assim como número de camadas. Seguindo a teoria de vigas espaciais e parametrizando a geometria, a linha média de apenas uma dessas hélices foi analisada analiticamente. Essa simplificação é valida visto que o contato e deslizamento não são incluídos nesta teoria, produzindo uma primeira abordagem ao problema da modelagem dessas estruturas. Sendo assim, as equações de equilíbrio foram deduzidas e seu sistema diferencial foi resolvido com o objetivo de representar o comportamento mecânico da estrutura. Utilizando a tríade de Frenet-Serret para definir um sistema de coordenadas local, as condições de contorno foram aplicadas buscando determinar as constantes de integração resultantes da solução analítica das equações diferenciais. Essa solução foi comparadas com resultados numéricos obtidos pelo Método dos Elementos Finitos (FEM) para validação dos casos de carga concentrada e distribuída em duas geometrias, o arco plano e a hélice. Em ambos os casos resultados apresentaram boa concordância para forças, momentos, rotações e deslocamentos. Considerando o caso do arco, o seu raio foi aumentado, de forma que a geometria se aproximasse de uma viga reta. O modelo proposto também foi utilizado para simular uma mola sob compressão. / A high number of structures uses cables due to their ability to bear large load in the longitudinal direction, for example, prestressed concrete, offshore systems and bridges. Its basic structure is formed by a central straight element surrounded by strands laid helically. A variety of geometries can be used, as well as the number of layers. Using the theory of spatial beams and parameterizing the geometry, the center line of only one of these helixes was analyzed analytically, since contact and slip are not included in this theory, obtaining a first approach in order to model these structures and to determine its mechanical behavior. Thus, the equilibrium equations were deduced and the differential system was solved with the objective of representing the mechanical behavior of the structure. Using the Frenet-Serret triad to define a local coordinate system, the boundary conditions were applied aiming the determination of the integration constants. The expressions obtained were compared with results obtained by the Finite Element Method (FEM) for validation applying concentrated and distributed loads. All cases presented good agreement FOR forces, moments, rotations and displacements. Considering the arc case, its radius was increased until a straight beam. The proposed model was also used to simulate a spring under compression.