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Torsion of cylindrical shafts has long been a basic subject in the classical theory of elasticity. In 1998 Swanson proposed a theoretical solution for the torsion problem of laminated composites. He adopted the traditional formulation of the torsion problem based on Saint Venant's torsion theory. The eigenfunction expansion method was employed to solve the formulated problem. The analytical method is proposed in this study enabling one to solve the torsion problem of laminated composite beams. Instead of following the classical Saint Venant theory formulation, the notion of effective elastic constant is utilized. This approach uses the concept of elastic constants, and in this context the three-dimensional non-homogeneous orthotropic laminate is replaced by an equivalent homogeneous orthotropic material. By adopting the assumptions of constant stress and constant strain, the effective shear moduli of the composite laminates are then derived. Upon obtaining the shear moduli of the equivalent homogeneous material, the effective torsional rigidity of the laminated composite rods can be determined by employing the theory developed by Lekhnitskii in 1963. Finally, the predicted results based on the present analytical approach are compared with those by the finite element, the finite difference method and Swanson's results. / Master of Science

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18044号 / 理博第3922号 / 新制||理||1566(附属図書館) / 30902 / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授 浅岡 正幸, 教授 加藤 毅, 教授 藤原 耕二 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

The standard grid bracing problem has a nice solution via the brace graph. If we introduce a window by removing an interior vertex of the grid, this solution comletely breaks down. We examine a 6 x 10 unit grid with a 2 x 2 window and provide an optimal solution via the Rigidity Matrix.

The Swedish law tells us that employers and co-workers are responsible to encourage gender equality work in order to make equal opportunities for both women and men in the Swedish work force. Different organizations have different conditions to change and the gender equality work is an example of a work of change. Previous research shows that gender equality work come across opposition in several ways. The aim of this study is to explain how departmental managers in care units work with gender equality and furthermore how the organization gives them conditions to do so. The question I aim to answer is: How is the departmental managers gender equality work influenced by the organizations particular conditions? To fulfil the aim of the study and answer the question I used a qualitative approach. Four departmental managers in care units were interviewed by means of semi- structured interviews. The material was processed with a thematic approach. I searched for common themes in the interviews and interpreted it with the assistance of select theory. The theories were Göran Ahrnes and Apostolis Papakostas organization theory about mechanisms of rigidity and Yvonne Hirdmans concept gender system. The results of the study show that written gender equality documents make mechanisms of rigidity and contribute to an inability to change. The organizations give the departmental managers capacity to diminish the need of gender equality work by means of shifting in time, category and responsibility. The analysis gives an explanation of the conditions with the assistance of the gender systems involvement in the organizations structure and culture. The conclusion means that the gender system makes the gender-differentiated organization inartificial, and therefore affects the conditions of the departmental managers gender equality work.

Sem dúvida a questão central em Dinâmica Holomorfa é aquela sobre a densidade de hiperbolicidade. Temos a seguinte conjectura devida a Pierre Fatou: No espaço das aplicações racionais de grau d o conjunto das aplicações racionais hiperbólicas neste espaço formam um subconjunto aberto e denso. Nem mesmo para a família dos polinômios quadráticos esta questão foi respondida. Para a família quadrática este problema é equivalente a mostrar a não existência de polinômios quadráticos que suportam sobre o seu conjunto de Julia um campo de linhas invariante. Devido a resultados de Jean-Christophe Yoccoz sabemos da não existência de campos de linhas invariante para polinômios quadráticos no máximo finitamente renormalizáveis. Nesta dissertação é mostrado que um polinômio quadrático infinitamente renormalizável satisfazendo certa hipótese geométrica, denominada robustez, não suporta sobre o seu Julia um campo de linhas invariante. Esta prova foi obtida por Curtis T. McMullen e publicada em [McM1]. Os avanços na teoria de renormalização e quanto ao problema da densidade de hiperbolicidade e problemas relacionados tem contado com a colaboração de inúmeros renomados matemáticos como Mikhail M. Lyubich, Artur Ávila, Mitsuhiro Shishikura, Curtis T. McMullen, Jean-Christophe Yoccoz, Sebastien van Strien, Hiroyuki Inou, dentre outros / Undoubtedly one of the central open questions in Holomorphic Dynamics is about proving the density of hyperbolicity. That question was first raised by Pierre Fatou: In the space of rational functions of degree d the set of hyperbolic rational functions form a open and dense subset. Not even for the family of quadratic polynomials this question been answered. For this particular quadratic family the problem is equivalent to showing the non-existence of quadratic polynomial with a Julia set supporting an invariant line field. Due to results by Jean-Christophe Yoccoz we already know the non-existence of invariant line fields for the quadratic polynomials that are at most finitely renormalizable. In this dissertation it is shown that an infinitely renormalizable quadratic polynomial satisfying a certain geometric hypotesis, called robustness, does not have an invariant line field supported on its Julia set. This proof was obtained by Curtis T. McMullen and published in [McM1]. Many advances on the theory of renormalization and on the problem of density of hyperbolicity have been already accomplished through the collective work of several renowned mathematicians such as Mikhail M. Lyubich, Artur Ávila, Mitsuhiro Shishikura, Curtis T. McMullen, Jean-Christophe Yoccoz, Sebastien van Strien, Hiroyuki Inou among others.

abstract: The rigidity of a material is the property that enables it to preserve its structure when deformed. In a rigid body, no internal motion is possible since the degrees of freedom of the system are limited to translations and rotations only. In the macroscopic scale, the rigidity and response of a material to external load can be studied using continuum elasticity theory. But when it comes to the microscopic scale, a simple yet powerful approach is to model the structure of the material and its interparticle interactions as a ball$-$and$-$spring network. This model allows a full description of rigidity in terms of the vibrational modes and the balance between degrees of freedom and constraints in the system. In the present work, we aim to establish a microscopic description of rigidity in \emph{disordered} networks. The studied networks can be designed to have a specific number of degrees of freedom and/or elastic properties. We first look into the rigidity transition in three types of networks including randomly diluted triangular networks, stress diluted triangular networks and jammed networks. It appears that the rigidity and linear response of these three types of systems are significantly different. In particular, jammed networks display higher levels of self-organization and a non-zero bulk modulus near the transition point. This is a unique set of properties that have not been observed in any other types of disordered networks. We incorporate these properties into a new definition of jamming that requires a network to hold one extra constraint in excess of isostaticity and have a finite non-zero bulk modulus. We then follow this definition by using a tuning by pruning algorithm to build spring networks that have both these properties and show that they behave exactly like jammed networks. We finally step into designing new disordered materials with desired elastic properties and show how disordered auxetic materials with a fully convex geometry can be produced. / Dissertation/Thesis / Doctoral Dissertation Physics 2018

This work is a compilation of structural results for the von Neumann algebras of poly-hyperbolic groups established in a series of works done jointly with I. Chifan and T. Sinclair; and S. Pant. These works provide a wide range of circumstances where the product structure, a discrete structural property, can be recovered from the von Neumann algebra (a continuous object). The primary result of Chifan, Sinclair and myself is as follows: if Γ = Γ1 × · · · × Γn is a product of non-elementary hyperbolic icc groups and Λ is a group such that L(Γ)=L(Λ), then Λ decomposes as an n-fold product of infinite groups. This provides a group-level strengthening of the unique prime decomposition of Ozawa and Popa by eliminating any assumption on the target group Λ. The methods necessary to establish this result provide a malleable procedure which allows one to rebuild the product of a group from the algebra itself. Modifying the techniques found in the previous work, Pant and I are able to demonstrate that the class of poly-groups exhibit a similar phenomenon. Specifically, if Γ is a poly-hyperbolic group whose corresponding algebra is non-prime, then the group must necessarily decompose as a product of infinite groups.

Shear walls are the primary lateral load resisting elements in bearing wall systems used in masonry construction. Horizontal loads due to wind or earthquake are transferred to vertical walls by diaphragms that are rigid such as concrete floor slabs or flexible such as wood floors. With rigid diaphragms, loads are apportioned to the supporting walls based on their relative rigidity. Walls with openings accommodating doors and windows (“perforated walls”) have reduced rigidity that can be determined using available hand calculation methods. These methods primarily focus on analysis procedures, not on the visualization of the load path that is critically important in structural engineering practice. The analogy of springs in series or parallel is used to determine the equivalent stiffness of elastic systems in structural dynamics. This thesis uses this analogy to develop a method that can help visualize load flow in perforated shear walls connected to rigid diaphragms. Rigidities are calculated using existing methods and combined as springs in series or parallel to represent a perforated wall. Loads taken by the wall segments correspond to the electrical current flowing through this imaginary “circuit”. To help visualize the load path, the line drawing representation of springs in series or parallel and the applied lateral load are deliberately oriented in the vertical direction. The application of the analogy is illustrated by several numerical examples of varying complexity taken from text books. Finite element solutions are included in the comparisons to provide a measure of the relative accuracy of hand calculation methods. The analogy can be extended to refine existing hand calculation methods though this increases computational effort. It improves accuracy but only for cases where the aspect ratio of the wall segments is such that shear effects are dominant.

The thesis is divided in three parts based largely on published articles or on manuscripts submitted for publication. First we propose a new method which is called the shooting-bead method. This method is a fast and easy experimental technique for evaluating cantilever stiffness and flexural rigidity of semi-flexible to semi-rigid rod-like biological and nano-filaments based on the measurement of just two distances. The method is based on applying a force normal to the filament with a microsphere bead trapped in the laser tweezer followed by its sudden release. Through a simple measurement of the distances that the bead moves, the flexural rigidity of the filament can be found from the formula derived in this paper. Then we take into account the effects of the viscous drag force exerted on the filament itself. To this end, we have defined a key variable, called the filament energy-loss factor (or filament drag factor) that accounts for all the energy-loss effects. It has been shown that the effect due to the consideration of filament energy-loss factor on calculation of the flexural rigidity increases with increasing the flexibility of the filament. Finally, in the third part we discuss the effect of ultrasound on the microtubules. Here we have analytically solved equations of motion for the vibrational dynamics of an MT that is attached at its two ends. This is especially relevant for MTs during mitosis when they attach to chromosomes and centrosomes. Our analysis applies to MTs present inside a viscous solution and when driven by an ultrasound plane wave. We have shown that with using ultrasound plane waves the resonance condition for the MT treated as a rigid rod cannot be provided, and in order to achieve resonance we should excite a single mode of the MT with a harmonic number larger than a threshold value introduced in this thesis. Single mode excitation not only helps to transfer the minimum amount of energy to the surrounding medium compared with multi-mode excitation but it also allows for a simultaneous high-amplitude and high-quality factor which is impossible when using plane waves.