Thin structures exist as one dimensional slender objects (hairs, tendrils, telephone cords, etc.) and two dimensional thin sheets (tree leaves, Mobius bands, eggshells, etc.). Geometric and material nonlinearities can conspire together to create complex phenomena in thin structures. This dissertation studies snap-through, multi-stability, and localization in thin rods and sheets through a combination of experiments and numerics. The first work experimentally explores the multi-stability and bifurcations of buckled elastic strips subject to clamping and lateral end translations, and compares these results with numerical continuation of a perfectly anisotropic Kirchhoff rod model. It is shown that this naive Kirchhoff rod model works surprisingly well as an organizing framework for thin bands with various widths. Thin sheets prefer to bend rather than to stretch because of the high cost of stretching energy. Knowing the bending response of thin sheets can aid in simulating deformations such as creasing. The second work introduces an exact pure bending linkage mechanism for potential use in a bend tester that measures the moment-curvature relationship of soft sheets and filaments. Mechanical rotary pleating is a bending-deformation-dominant process that deforms nonwoven materials into zigzag filter structures. The third work studies what combinations of processing and material parameters lead to successful rotary pleating. The rotary pleating process is formulated as a multi-point variable-arc-length boundary value problem for an inextensible rod, with a moment-curvature constitutive law, such as might be measured by a bend tester, as input. Through parametric studies, this work generates pleatability surfaces that may help avoid pleating failure in the real pleating process. Creased thin sheets are generally bistable. The final work of this dissertation studies bistability of creased thin disks under the removal of singularities. A hole is cut in the disk and, through numerical continuation of an inextensible strip model, this work studies how the crease stiffness, crease angle, and hole geometry affect the bistability. / Doctor of Philosophy / Thin structures are those that have at least one dimension smaller than the other dimensions, such as hairs, telephone cords, and tree leaves, to name just a few. They can generate rich mechanical behaviors (e.g., snapping, crumpling) and complex shapes. A simple example is to rotate the two ends of a thin strip that has been deformed into an arch. Snapping will happen at a certain rotation angle. The first work studies snapping behaviors of thin bands subject to rotations and displacements at the two ends. This work employs a mechanical model based on force and moment balance on a spatial curve to solve the shapes of thin strips and capture the rich snapping behaviors. It is much harder to stretch a thin sheet than to bend it, which can be easily seen by deforming a piece of paper. The physics behind this is that stretching requires more energy than bending in thin objects. Knowing the bending response of thin sheets can aid in simulating deformations of thin structures. The second work introduces a new pure bending mechanism that can subject a sheet to pure bending and measure its bending response through a moment-curvature relationship. Thin sheets find broad applications in engineering. Mechanical pleating is a long-standing technique that deforms thin sheets into zigzag filter structures, but the mechanics behind it is unclear. The third work studies a rotary pleating process and aims to answer a basic question: What combinations of processing and material parameters lead to successful pleating? This work employs a one-dimensional model of an inextensible rod, with a moment-curvature constitutive law as input. The moment-curvature relationship of pleating materials can be measured by the pure bending mechanism developed in the second work. Thin sheets with prescribed crease patterns can create complicated and targeted shapes, such as origami (paper folding) and kirigami (paper cutting). A simple creased thin sheet is bistable: A stable configuration can be obtained by inverting the crease, which leads to a conical vertex/singularity. The fourth work of this dissertation finds that the bistability of creased thin sheets will be destroyed if a large hole is made around the vertex. This work studies the loss of bistability of creases under removal of singularities by quantifying how the hole size, hole geometry, and other factors such as the crease angle and crease stiffness affect the bistability.

Dauguma mašinų ir mechanizmų detalių eksploatacijos metu veikiamos lenkimu. Esant trumpalaikėms perkrovoms, ypatingai įrengimų paleidimo ir stabdymo metu, šiose detalėse gali atsirasti tampriai plastinis įtempių - deformacijų būvis. Kadangi tokios perkrovos dažniausiai periodiškai kartojasi, detalės ar jų atskiri elementai patiria ciklinį tampriai plastinį deformavimą, kuris gali baigtis suirimu. Šiame darbe pateikiamas skritulinio skerspjūvio strypo statinio tampriai plastinio grynojo lenkimo analitinių priklausomybių, naudojant laipsninę įtempių-deformacijų kreivės plastinės dalies aproksimaciją, išvedimas. Gautos priklausomybės įvertina mechaninių medžiagos charakteristikų skirtumus tempimo ir gniuždymo atveju, jos gali būti naudojamos apskaičiuojant įtempių neutraliojo sluoksnio padėties pokyčiams deformavimo metu bei nustatant lenkimo momento ir didžiausios strypo deformacijos priklausomybę. Pateiktos priklausomybės gali būti pritaikytos ir cikliniam tampriai plastinio grynojo lenkimo analitiniam tyrimui. / In real condition a great majority of machines and structure elements are subjected to bending. Occasionally, such an element can be overloaded and its stress strain state exceeds the proportional limit. That’s why the study of elastic-plastic bending has a wide engineering science background and a very broad field of application. This work presents analytical research of circular cross-section element under pure bending. The simple power relation of stress and strain response in the region of plastic deformation is used. The relationships describing non-dimensional deviation of the stress neutral axis from symmetry axis of an element and non-dimensional monotonic bending moment are presented. Results of theoretical analysis are compared with experimental date. Derived relationships can be also fitted to analysis of circular cross-section element loaded by low cycle pure bending.

In real conditions, a great majority of machine and structure elements and parts (shafts, pins, axis, etc.) are subjected to bending. That’s why the study of elastic plastic bending has a wide engineering science background and a very broad field of application. This work presents analytical research of elastic plastic pure bending of rectangular cross-section element. The simple power relation expresses stress strain curve in the region of uniform plastic deformation. Derived mathematical relations allow to calculate deviation of dimensionless stress neutral axis from symmetry axis of an element and dimensionless pure bending moment versus monotonic strain. Theoretical curves for different material constants are drawn. Theoretical curves of dimensionless pure bending moment give tolerable coincidence with experimental date. Derived relationships can be also fitted to analysis of rectangular cross-section element loaded by low cycle pure bending.

Bending of thin-walled tubing to a prescribed bend radius is typically performed by bending it around a mandrel of the desired bend radius, corrected for spring back. By eliminating the mandrel, costly setup time would be reduced, permitting multiple change of radius during a production run, and even intermixing different products on the same line. The principal challenge is to avoid buckling, as the mandrel and shoe are generally shaped to enclose the tube while bending. Without the shaped mandrel, buckling will likely occur sooner, that is, at larger bend radii. A test apparatus has been built for arborless bending. It has been used to determine the limits of bend radius, wall thickness, material properties, etc. on buckling. Key to the process is a set of moveable clamps, which grip the tube and rotate to produce the bend. A complex control system moves the clamps radially to maintain pure bending, without superimposing tension or compression. A series of tests were performed to document the safe region of operation to avoid buckling. Charts have been created to assist the operator, as well as the design engineer, in determining the minimum bend radius. Similar tests will be required for each additional tube size, thickness, material, etc.

The modified mapping-collocation (MMC) method is applied to analyze a circumferential crack in an isotropic curved beam. Based on the method a MATLAB code was developed to obtain the stress field. Incorporating the stress correlation technique, the opening and sliding fracture mode stress intensity factors (SIF)s of the crack for the beam under pure bending moment load case are calculated. The MMC method aims to solve two-dimensional problems of linear elastic fracture mechanics (LEFM) by combining the power of analytic tools of complex analysis (Muskhelishvili formulation, conformal mapping, and extension arguments) with simplicity of applying the boundary collocation method as a numerical solution approach. Qualitatively, a good agreement between the computed stress contours and the fringe shapes obtained from the photoelastic experiment on a plexiglass specimen is observed. Quantitatively, the results are compared with that of ANSYS finite element analysis software. The effect of crack size, crack position and beam thickness variation on SIF values and mode mixity is investigated.

Dagens samhälle har fått en explosiv utveckling som förverkligar mycket som för bara några år sedan var inte mer än fantasier.  Dagens utvecklingsförsprång ställer oss, byggnadskonstruktörer, inför rejäla utmaningar. Den globala folktillväxten ökar väsentligt vilket leder till tätbefolkade städer. Detta utvecklar ett stort utrymmesbehov hos många av oss. Allt detta resulterar i att efterfrågan på stora och öppna planlösningar ökar markant. En av dagens tendenser är att beställare och arkitekter har en benägenhet att tänja på gränserna på maximala spännvidder mellan bärande betongväggar, för bjälklagstjockleken 250 mm. Detta är ett tillfredsställande mått för att klara ljudklass B. Dessutom är det opraktiskt att variera bjälklagstjocklekar inom ett projekt, därför vill man ha uniformitet med samma tjocklek över projektet. För att vi ska kunna förverkliga vårt uppdrag har vi varit tvungna att genomgå en lång beräknings- och undersökningsprocess. I våra beräkningar har vi lagt fokus på två upplagsfall. Det första upplagsfallet ”fri-inspänd” och det andra fallet ”inspänd-yttre gavelvägg”. Första fallet har varit det värsta fallet i och med att vi bara har ett stöd som måste bära hela betongbjälklaget, vilket har varit en stor utmaning. Andra fallet var dock betydligt enklare på grund av de två stöden som utgjorde en stor del av ”arbetet” och lyfter upp bjälklaget, hela tyngden vilade inte på armeringen som i föregående fall. Inte bara spännvidden skall klaras utan även angiven sprickvidd på 0,3 mm. Examensarbetet består av förklarande fakta som är strikt relaterad till efterföljande beräkningar. Alla beräkningar har utförts för hand, utan programstöd. / Today's society has received a degenerate development embodying much that just a few years ago was no more than fantasies. This development sets us, structural engineers, facing real challenges. The global population growth increases significantly leading to densely populated cities. This develops a large space need for many of us. All this results in the increasing demand for large and open floor plans significantly. One of the current trends is that the clients and architects have a tendency to push the limits on maximum spans between bearing concrete walls, slabs for thickness 250 mm. This is a satisfactory measure of the concrete content to manage audio class B. Moreover, it is impractical to vary the slab thickness within a project, so he wants to have uniformity with the same thickness over the project. For us to be able to realize these long spans between bearing walls, we have been forced to undergo a long calculation and examination process. To begin with, we have studied the company's requirements and preferences, based on that, we started joists analysis. In our calculations, we have laid emphasis on two cases. The first circulation fall "free - clamped" and the second, "clamped- outer end wall." The first case has been the worst case, in that we only have one support that must bear the entire concrete slab, which has been a major challenge. Second case was considerably easier due to the two supports which made a large part of "work" and lifts the slab, the full weight rested not on the reinforcement as in the previous case. Not just the span must be met, but also given crack width of 0.3 mm. The thesis consists of explanatory facts that are strictly related to the subsequent calculations. All calculations have been performed by hand, without program support.

The aim of the thesis is the investigation of fracture-mechanics parameters on specimens made of quasi-brittle materials. The principles of two-parameter fracture mechanics are used. Couple of numerical simulations were done and their outputs are used for two main analysed specimen geometries. For simulations the finite element method software ANSYS is used. In the first part, the thesis focuses on bended specimens. The influence of different geometric parameters on fracture mechanics behaviour of cracked specimen is investigated. For model calibration the outputs of other authors are used. In the second part the specimens for modified compact-tension test (CT test) are analysed. Similar to the first part, the influence of geometric parameters of the specimen (in this case, the specimen size) on fracture mechanics parameters were investigated. The modified CT test was derived from CT test which is commonly used for metal materials testing as the suitable geometry for cement-based composite materials testing. The outputs of both parts are calibration polynomials, which are expressions obtained for different specimen geometries, giving the value of fracture mechanics parameter as the function of specimen geometry. As the example, calibration curves are used to obtain fracture toughness of tested material using the outputs from recent experiment.