A short note on a Bernstein-Bezier basis for the pyramid

We introduce a Bernstein-Bezier basis for the pyramid, whose restriction to the face reduces to the Bernstein-Bezier basis on the triangle or quadrilateral. The basis satisfies the standard positivity and partition of unity properties common to Bernstein polynomials, and spans the same space as non-polynomial pyramid bases in the literature.Comment: Submitte

Optimal higher order modeling methodology based on method of moments and finite element method for electromagnetics

2011 Fall.Includes bibliographical references.General guidelines and quantitative recipes for adoptions of optimal higher order parameters for computational electromagnetics (CEM) modeling using the method of moments and the finite element method are established and validated, based on an exhaustive series of numerical experiments and comprehensive case studies on higher order hierarchical CEM models of metallic and dielectric scatterers. The modeling parameters considered are: electrical dimensions of elements (subdivisions) in the model (h-refinement), polynomial orders of basis and testing functions (p-refinement), orders of Gauss-Legendre integration formulas (numbers of integration points - integration accuracy), and geometrical orders of elements (orders of Lagrange-type curvature) in the model. The goal of the study, which is the first such study of higher order parameters in CEM, is to reduce the dilemmas and uncertainties associated with the great modeling flexibility of higher order elements, basis and testing functions, and integration procedures (this flexibility is the principal advantage but also the greatest shortcoming of the higher order CEM), and to ease and facilitate the decisions to be made on how to actually use them, by both CEM developers and practitioners. The ultimate goal is to close the large gap between the rising academic interest in higher order CEM, which evidently shows great numerical potential, and its actual usefulness and application to electromagnetics research and engineering applications

Geometrically Exact and Analysis Suitable Mesh Generation Using Rational Bernstein–Bezier Elements

This dissertation presents two novel contributions to the fields of isogeometric analysis and p-version finite elements. First, we present a framework for geometrically exact volumetric mesh generation. By leveraging ideas from both traditional mesh generation as well as isogeometric analysis, we develop a framework for volumetric mesh generation using rational Bernstein--Bézier discretizations. Within this framework, we provide a set of easily verifiable sufficient conditions for guaranteeing that a mesh will be geometrically exact. Second, we develop a complete theory of mesh quality for these rational Bernstein--Bézier elements. From this, we derive a set of easily computable mesh quality metrics for verifying that a rational Bernstein--Bézier discretization will be analysis suitable

The grammar of developable double corrugations (for formal architectural applications)

This paper investigates the geometrical basis of regular corrugations, with specific emphasis on Developable Double Corrugations (DDCs), which form a unique sub-branch of Origami Folding and Creasing Algorithms. The aim of the exercise is three fold – (1) To define and isolate a ‘single smallest starting block’ for a given set of distinct and divergent DDC patterns, such that this starting block becomes the generator of all DDCs when different generative rules are applied to it. (2) To delineate those generic parameters and generative rules which would apply to the starting block, such that different DDCs are created as a result (3) To use the knowledge from points (1) and (2) to create a complete family of architectural forms and shapes using DDCs. For this purpose, a matrix of 12 underlying geometry types are identified and used as archetypes. The objective is to mathematically explore DDCs for architectural form finding, using physical folding as a primary algorithmic tool. Some DDCs have more degrees of freedom than others and can fit varied geometries, while others cannot. The discussion and conclusions involve - (a) identifying why certain DDCs are ideal for certain forms and not others, when all of them are generated using the same/or similar starting block(s), (b) discussing the critical significance of flat-foldability in this specific context and (c) what we can do with this knowledge of DDCs in the field of architectural research and practice in the future

Formulation of constitutive relations based on indentation test

Ph.DDOCTOR OF PHILOSOPH

Material characterization via simulated indentation test including effect of friction

Ph.DDOCTOR OF PHILOSOPH

Nonlinear finite element treatment of bifurcation in the post-buckling analysis of thin elastic plates and shells

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The geometrically nonlinear constant moment triangle based on the von Karman theory of thin plates is first described. This finite element, which is believed to be the simplest possible element to pass the totality of the von Karman patch test, is employed throughout the present work. It possesses the special characteristic of providing a tangent stiffness matrix which is accurate and without approximation. The stability of equilibrium of discrete conservative systems is discussed. The criteria which identify the critical points (limit and bifurcation), and the method of determination of the stability coefficients are presented in a simple matrix formulation which is suitable for computation. An alternative formulation which makes direct use of higher order directional derivatives of the total potential energy is also presented. Continuation along the stable equilibrium solution path is achieved by using a recently developed Newton method specially modified so that stable points are points of attraction. In conjunction with this solution technique, a branch switching method is introduced which directly computes any intersecting branches. Bifurcational buckling often exhibits huge structural changes and it is believed that the computation of the required switch procedure is performed here, and for the first time, in a satisfactory manner. Hence, both limit and bifurcation points can be treated without difficulty and with continuation into the post buckling regime. In this way, the ability to compute the stable equilibrium path throughout the load-deformation history is accomplished. Two numerical examples which exhibit bifurcational buckling are treated in detail and provide numerical evidence as to the ability of the employed techniques to handle even the most complex problems. Although only relatively coarse finite element meshes are used it is evident that the technique provides a powerful tool for any kind of thin elastic plate and shell problem. The thesis concludes with a proposal for an algorithm to automate the computation of the unknown parameter in the branch switching method.Procurement Executive of the Ministry of Defence (Strategic Research Programme AS011D02

A symmetry analysis off early mediaeval ormameimtation

The aim of this thesis is to test the appropriateness of symmetry analysis as a method for the systematic classification of Early Mediaeval ornamentation. This method is different from the traditional Montehan concept of formal classification in archaeology, in that the stylistic entities are not chosen according to the formal similarity of individual motifs and motif-elements, but according to the formal similarity of their symmetrical organisation within an ornamental pattern. It is suggested that symmetry analysis is a more objective method of classifying and analysing ornamentation, as it avoids the subjective selection of typological elements, and therefore also avoids one of the pitfalls of typological classification caused by the ambiguity of the concept of style. Washburn, the originator of this method has suggested that in this way hypotheses can be tested regarding the identity as well as the interaction or information exchange of individuals belonging to a certain cultural, ethnic or social group. In order to test the usefulness of symmetry analysis in relation to these proposals for archaeological research, garnet jewellery from the Merovingian period as well as two manuscript paintings from the Gospel-books of Lindisfarne and Kells have been analysed and compared. It was concluded that the structure of the design-fields of the different types of artefact is one of the main factors for the appearance of certain symmetries within the ornamental context of the artefacts. However, the analysis could also indicate that the method has the potential to classify decorated artefacts according to different regions and workshops of production, and even according to their different social milieu of production. It is concluded that a larger quantity of material has to be analysed in order to get conclusive results from the symmetrical analysis in relation to the latter aspects of investigation, and with regard to the other original proposals made by Washburn

Hierarchical component-wise models for enhanced stress analysis and health monitoring of composites structures

L'abstract è presente nell'allegato / the abstract is in the attachmen