scholarly journals Geometric Formulation of BRS and BRS* Transformations in T4 Theory

1984 ◽  
Vol 71 (1) ◽  
pp. 174-182
Author(s):  
H. Kikukawa ◽  
J. Kikukawa
Keyword(s):  
Geometric Formulation

A New Stress-Intensity Factor Solution for an External Surface Crack in Spheres

2021 ◽  
Author(s):  
James C. Sobotka ◽  
Yi-Der Lee ◽  
Joseph W. Cardinal ◽  
R. Craig McClung
Keyword(s):  
Stress Intensity Factor ◽  
Finite Element ◽  
Crack Front ◽  
Surface Crack ◽  
Degrees Of Freedom ◽  
External Surface ◽  
Crack Plane ◽  
Finite Element Analyses ◽  
Stress Variations ◽  
Geometric Formulation

Abstract This paper describes a new stress-intensity factor (SIF) solution for an external surface crack in a sphere that expands capabilities previously available for this common pressure vessel geometry. The SIF solution employs the weight function (WF) methodology that enables rapid calculations of SIF values. The WF methodology determines SIF values from the nonlinear stress variations computed for the uncracked geometry, e.g., from service stresses and/or residual stresses. The current approach supports two degrees of freedom that denote the two crack tips located normal to the surface and the surface of the sphere. The geometric formulation of this solution enforces an elliptical crack front, maintains normality of the crack front with the free surface, and supports two degrees of freedom for fatigue crack growth from an internal crack tip and a surface crack tip. The new SIF solution accommodates spherical geometries with an exterior diameter greater than or equal to four times the thickness. This WF SIF solution has been combined with stress variations common for spherical pressure vessels: uniform internal pressure on the interior surface, uniform tension on the crack plane, and uniform bending on the crack plane. This paper provides a complete overview of this solution. We present for the first time the geometric formulation of the crack front that enables the new functionality and set the geometric limits of the solution, e.g., the maximum size and shape of the crack front. The paper discusses the bivariant WF formulation used to define the SIF solution and details the finite element analyses employed to calibrate terms in the WF formulation. A summary of preliminary verification efforts demonstrates the credibility of this solution against independent results from finite element analyses. We also compare results of this new solution against independent SIFs computed by finite element analyses, legacy SIF solutions, API 579, and FITNET. These comparisons indicate that the new WF solution compares favorably with results from finite element analyses. This paper summarizes ongoing efforts to improve and extend this solution, including formal verification and development of an internal surface crack model. Finally, we discuss the capabilities of this solution’s implementation in NASGRO® v10.0.

scholarly journals The one-loop tadpole in the geoSMEFT

2021 ◽  
Vol 11 (5) ◽  
Author(s):  
Tyler Corbett
Keyword(s):  
Field Theory ◽  
Standard Model ◽  
Effective Field Theory ◽  
Effective Field ◽  
Power Counting ◽  
Leading Order ◽  
The Standard Model ◽  
The One ◽  
Near Future ◽  
Geometric Formulation

Making use of the geometric formulation of the Standard Model Effective Field Theory we calculate the one-loop tadpole diagrams to all orders in the Standard Model Effective Field Theory power counting. This work represents the first calculation of a one-loop amplitude beyond leading order in the Standard Model Effective Field Theory, and discusses the potential to extend this methodology to perform similar calculations of observables in the near future.

Geometry-Based Thick Origami Simulation

2020 ◽  
Vol 143 (6) ◽  
Author(s):  
Tsz-Ho Kwok
Keyword(s):  
Three Dimensional ◽  
Geometric Design ◽  
Experimental Results ◽  
Engineering Applications ◽  
3D Shape ◽  
Folding Paper ◽  
Geometric Simulation ◽  
Geometric Formulation

Abstract Origami is the art of creating a three-dimensional (3D) shape by folding paper. It has drawn much attention from researchers, and the designs that origami has inspired are used in various engineering applications. Most of these designs are based on familiar origami patterns and their known deformations, but origami patterns were originally intended for materials of near-zero thickness, primarily paper. To use the designs in engineering applications, it is necessary to simulate origami in a way that enables designers to explore and understand the designs while taking the thickness of the material to be folded into account. Because origami is primarily a problem in geometric design, this paper develops a geometric simulation for thick origami. The actuation, constraints, and assignment of mountain and valley folds in origami are also incorporated into the geometric formulation. The experimental results show that the proposed method is efficient and accurate. The method can successfully simulate a flat-foldable degree-four vertex, two different action origami, the bistable property of a waterbomb base, and the elasticity of non-rigid origami panels.

Geometric Simulation for Thick Origami

2019 ◽  
Author(s):  
Tsz-Ho Kwok
Keyword(s):  
Design Problem ◽  
Three Dimensional ◽  
Experimental Results ◽  
Engineering Applications ◽  
Research Attention ◽  
3D Shape ◽  
Mountain Valley ◽  
Geometry Design ◽  
Geometric Simulation ◽  
Geometric Formulation

Abstract Origami is an art that creates a three-dimensional (3D) shape only by folding. This capability has drawn much research attention recently, and its applied or inspired designs are utilized in various engineering applications. Most current designs are based on the existing origami patterns and their known deformation, but origami patterns are universally designed for zero-thickness like a paper. To extend the designs for engineering applications, simulation of origami is needed to help designers explore and understand the designs, and the simulation must take the material thickness into account. With the observation that origami is mainly a geometry design problem, this paper develops a geometric simulation for thick origami, similar to a pseudo-physics approach. The actuation, constraints, and mountain/valley assignments of origami are also incorporated in the geometric formulation. Experimental results show that the proposed method is efficient and accurate. It can simulate successfully the bistable property of a waterbomb base, two different action origami, and the elasticity of origami panels when they are not rigid.

scholarly journals Geometric charges and nonlinear elasticity of two-dimensional elastic metamaterials

2020 ◽  
Vol 117 (19) ◽  
pp. 10195-10202
Author(s):  
Yohai Bar-Sinai ◽  
Gabriele Librandi ◽  
Katia Bertoldi ◽  
Michael Moshe
Keyword(s):  
Elastic Problem ◽  
Porous Solids ◽  
Two Dimensional ◽  
Mechanical Instability ◽  
Mechanical Metamaterials ◽  
Recent Developments ◽  
Elastic Metamaterials ◽  
Geometrical Effects ◽  
Nonlinear Geometric ◽  
Geometric Formulation

Problems of flexible mechanical metamaterials, and highly deformable porous solids in general, are rich and complex due to their nonlinear mechanics and the presence of nontrivial geometrical effects. While numeric approaches are successful, analytic tools and conceptual frameworks are largely lacking. Using an analogy with electrostatics, and building on recent developments in a nonlinear geometric formulation of elasticity, we develop a formalism that maps the two-dimensional (2D) elastic problem into that of nonlinear interaction of elastic charges. This approach offers an intuitive conceptual framework, qualitatively explaining the linear response, the onset of mechanical instability, and aspects of the postinstability state. Apart from intuition, the formalism also quantitatively reproduces full numeric simulations of several prototypical 2D structures. Possible applications of the tools developed in this work for the study of ordered and disordered 2D porous elastic metamaterials are discussed.

scholarly journals Geometric viewpoint on the quantization of a fuzzy logic

2020 ◽  
Vol 17 (13) ◽  
pp. 2050201
Author(s):  
Davide Pastorello
Keyword(s):  
Fuzzy Logic ◽  
Phase Space ◽  
Complex Projective Space ◽  
Product Formula ◽  
Kähler Structure ◽  
Set Operations ◽  
Logical Connectives ◽  
Standard Set ◽  
Complex Projective ◽  
Geometric Formulation

Within the Hamiltonian framework, the propositions about a classical physical system are described in the Borel [Formula: see text]-algebra of a symplectic manifold (the phase space) where logical connectives are the standard set operations. Considering the geometric formulation of quantum mechanics we give a description of quantum propositions in terms of fuzzy events in a complex projective space equipped with Kähler structure (the quantum phase space) obtaining a quantized version of a fuzzy logic by deformation of the product [Formula: see text]-norm.

Geometric Formulation of the Many-Electron Theory

2008 ◽  
Vol 18 (3-4) ◽  
pp. 807-841 ◽  
Author(s):  
Jaime Keller ◽  
Alejandro Keller
Keyword(s):  
Electron Theory ◽  
The Many ◽  
Geometric Formulation
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