Design of Self-Supporting Surfaces with Isogeometric Analysis

International audienceSelf-supporting surfaces are widely used in contemporary architecture, but their design remains a challenging problem. This paper aims to provide a heuristic strategy for the design of complex self-supporting surfaces. In our method, non-uniform rational B-spline (NURBS) surfaces are used to describe the smooth geometry of the self-supporting surface. The equilibrium state of the surface is derived with membrane shell theory and Airy stresses within the surfaces are used as tunable variables for the proposed heuristic design strategy. The corresponding self-supporting shapes to the given stress states are calculated by the nonlinear isogeometric analysis (IGA) method. Our validation using analytic catenary surfaces shows that the proposed method finds the correct self-supporting shape with a convergence rate one order higher than the degree of the applied NURBS basis function. Tests on boundary conditions show that the boundary's influence propagates along the main stress directions in the surface. Various self-supporting masonry structures, including models with complex topology, are constructed using the presented method. Compared with existing methods such as thrust network analysis and dynamic relaxation, the proposed method benefits from the advantages of NURBS-based IGA, featuring smooth geometric description, good adaption to complex shapes and increased efficiency of computation

A Solution of Plane Stress Problem Subjected to Horizontal Shear Force by Using Polynomial Airy Stress Function

Many structural analysis problems in civil engineering and mechanical engineering can be treated as plane stress and plane strain problems introduced in the theory of elasticity. One of the popular analytical methods to tackle plane analysis is to determine Airy stress function. In general, the Airy stress function depends on the analyzed domain and the applied loads; however, the number of problems that can be solved by employing this method is limited because of the formidable challenges of guessing trial function. In many cases, the trial Airy stress functions are selected based on the results of a simple beam model or experimental results. This paper introduces a solution of the plane stress subjected to horizontal shear forces by using a polynomial Airy stress function, in which the trail function is predicted from the results of the elementary beam theory of an equivalent model. The numerical investigation on stress distributions was presented, and it showed that although the internal shear force acting on cross-sections have not appeared, shear stress still appeared, and the shear stress diagram had both negative and positive areas

A Solution of Plane Stress Problem Subjected to Horizontal Shear Force by Using Polynomial Airy Stress Function

Many structural analysis problems in civil engineering and mechanical engineering can be treated as plane stress and plane strain problems introduced in the theory of elasticity. One of the popular analytical methods to tackle plane analysis is to determine Airy stress function. In general, the Airy stress function depends on the analyzed domain and the applied loads; however, the number of problems that can be solved by employing this method is limited because of the formidable challenges of guessing trial function. In many cases, the trial Airy stress functions are selected based on the results of a simple beam model or experimental results. This paper introduces a solution of the plane stress subjected to horizontal shear forces by using a polynomial Airy stress function, in which the trail function is predicted from the results of the elementary beam theory of an equivalent model. The numerical investigation on stress distributions was presented, and it showed that although the internal shear force acting on cross-sections have not appeared, shear stress still appeared, and the shear stress diagram had both negative and positive areas

Geometry-based structural analysis and design via discrete stress functions

This PhD thesis proposes a direct and unified method for generating global static equilibrium for 2D and 3D reciprocal form and force diagrams based on reciprocal discrete stress functions. This research combines and reinterprets knowledge from Maxwell’s 19th century graphic statics, projective geometry and rigidity theory to provide an interactive design and analysis framework through which information about designed structural performance can be geometrically encoded in the form of the characteristics of the stress function. This method results in novel, intuitive design and analysis freedoms. In contrast to contemporary computational frameworks, this method is direct and analytical. In this way, there is no need for iteration, the designer operates by default within the equilibrium space and the mathematically elegant nature of this framework results in its wide applicability as well as in added educational value. Moreover, it provides the designers with the agility to start from any one of the four interlinked reciprocal objects (form diagram, force diagram, corresponding stress functions). This method has the potential to be applied in a wide range of case studies and fields. Specifically, it leads to the design, analysis and load-path optimisation of tension-and compression 2D and 3D trusses, tensegrities, the exoskeletons of towers, and in conjunction with force density, to tension-and-compression grid-shells, shells and vaults. Moreover, the abstract nature of this method leads to wide cross-disciplinary applicability, such as 2D and 3D discrete stress fields in structural concrete and to a geometrical interpretation of yield line theory

Investigation of the Response of a Masonry Arch Railway Bridge using Membrane Equilibrium Analysis

This paper presents an application of Membrane Equilibrium Analysis (MEA) to a historic masonry arch railway bridge in Leeds, United Kingdom. This case study structure is representative of the many masonry arch bridges present on UK and European railway transport networks. It has been chosen because, since 2016, it has been the subject of a detailed Structural Health Monitoring (SHM) campaign, making it an ideal candidate against which to test analytic models. Typically, asset engineers will be responsible for maintaining a large stock of these structures and will lack the time to perform thorough computational analyses. Therefore, simplified approaches, such as MEA, which can offer insight into structural behaviour, have the potential to be highly valuable. This study represents the first step in applying MEA to masonry arch railway bridges

The architectural application of shells whose boundaries subtend a constant solid angle

Surface geometry plays a central role in the design of bridges, vaults and shells, using various techniques for generating a geometry which aims to balance structural, spatial, aesthetic and construction requirements. In this paper we propose the use of surfaces defined such that given closed curves subtend a constant solid angle at all points on the surface and form its boundary. Constant solid angle surfaces enable one to control the boundary slope and hence achieve an approximately constant span-to-height ratio as the span varies, making them structurally viable for shell structures. In addition, when the entire surface boundary is in the same plane, the slope of the surface around the boundary is constant and thus follows a principal curvature direction. Such surfaces are suitable for surface grids where planar quadrilaterals meet the surface boundaries. They can also be used as the Airy stress function in the form finding of shells having forces concentrated at the corners. Our technique employs the Gauss-Bonnet theorem to calculate the solid angle of a point in space and Newton's method to move the point onto the constant solid angle surface. We use the Biot-Savart law to find the gradient of the solid angle. The technique can be applied in parallel to each surface point without an initial mesh, opening up for future studies and other applications when boundary curves are known but the initial topology is unknown. We show the geometrical properties, possibilities and limitations of surfaces of constant solid angle using examples in three dimensions

Feasibility of a 30-meter space based laser transmitter

A study was made of the application of large expandable mirror structures in future space missions to establish the feasibility and define the potential of high power laser systems for such applications as propulsion and power transmission. Application of these concepts requires a 30-meter diameter, diffraction limited mirror for transmission of the laser energy. Three concepts for the transmitter are presented. These concepts include consideration of continuous as well as segmented mirror surfaces and the major stow-deployment categories of inflatable, variable geometry and assembled-in-space structures. The mirror surface for each concept would be actively monitored and controlled to maintain diffraction limited performance at 10.6 microns during operation. The proposed mirror configurations are based on existing aerospace state-of-the-art technology. The assembled-in-space concept appears to be the most feasible, at this time

Collapse capacity of masonry domes under horizontal loads: A static limit analysis approach

A static limit analysis approach is proposed for assessing the collapse capacity of axisymmetric masonry domes subject to horizontal forces. The problem formulation is based on the sound theoretical framework provided by the classical statics of shells. After introducing the shell stress tensors on the dome mid-surface, integral equilibrium equations are enforced for its typical part. Heyman's assumptions of infinite compressive and vanishing tensile strengths are made, with cohesionless friction behavior governing the shear strength, to characterize the admissible stress states in the dome. An original computational strategy is developed to address the resulting static limit analysis problem, involving the introduction of a mesh on the dome mid-surface, the interpolation of the physical components of the shell stress tensors on the element boundaries, and the imposition of equilibrium and admissibility conditions respectively for the elements and at the nodes of the mesh. The descending discrete convex optimization problem is solved by standard and effective optimization tools, automatically providing collapse multiplier of horizontal forces, incipient collapse mechanism and expected crack pattern. Convergence analysis, validation with experimental results available in the literature, and parametric analyses with respect to geometric parameters and friction coefficient, are presented for spherical and ellipsoidal masonry domes, proving the reliability of the proposed approach for estimating the pseudo-static seismic resistance of masonry domes.Comment: 29 pages, 11 figure

Roadmap on structured light

Structured light refers to the generation and application of custom light fields. As the tools and technology to create and detect structured light have evolved, steadily the applications have begun to emerge. This roadmap touches on the key fields within structured light from the perspective of experts in those areas, providing insight into the current state and the challenges their respective fields face. Collectively the roadmap outlines the venerable nature of structured light research and the exciting prospects for the future that are yet to be realized.Peer ReviewedPostprint (published version

Nonlinear and Quantum Optics with Whispering Gallery Resonators

Optical Whispering Gallery Modes (WGMs) derive their name from a famous acoustic phenomenon of guiding a wave by a curved boundary observed nearly a century ago. This phenomenon has a rather general nature, equally applicable to sound and all other waves. It enables resonators of unique properties attractive both in science and engineering. Very high quality factors of optical WGM resonators persisting in a wide wavelength range spanning from radio frequencies to ultraviolet light, their small mode volume, and tunable in- and out- coupling make them exceptionally efficient for nonlinear optical applications. Nonlinear optics facilitates interaction of photons with each other and with other physical systems, and is of prime importance in quantum optics. In this paper we review numerous applications of WGM resonators in nonlinear and quantum optics. We outline the current areas of interest, summarize progress, highlight difficulties, and discuss possible future development trends in these areas.Comment: This is a review paper with 615 references, submitted to J. Op