scholarly journals Simple deformation measures for discrete elastic rods and ribbons

2021 ◽  
Vol 477 (2256) ◽  
Author(s):  
K. Korner ◽  
B. Audoly ◽  
K. Bhattacharya
Keyword(s):  
Strain Energy ◽  
Alternative Formulation ◽  
Elastic Rod ◽  
Strain Gradients ◽  
Polygonal Chain ◽  
Elastic Bodies ◽  
Simple Deformation ◽  
Definition Of ◽  
Continuous Rod ◽  
Twisting Deformation

The discrete elastic rod method (Bergou et al. 2008 ACM Trans. Graph . 27 , 63:1–63:12. ( doi:10.1145/1360612.1360662 )) is a numerical method for simulating slender elastic bodies. It works by representing the centreline as a polygonal chain, attaching two perpendicular directors to each segment and defining discrete stretching, bending and twisting deformation measures and a discrete strain energy. Here, we investigate an alternative formulation of this model based on a simpler definition of the discrete deformation measures. Both formulations are equally consistent with the continuous rod model. Simple formulae for the first and second gradients of the discrete deformation measures are derived, making it easy to calculate the Hessian of the discrete strain energy. A few numerical illustrations are given. The approach is also extended to inextensible ribbons described by the Wunderlich model, and both the developability constraint and the dependence of the energy on the strain gradients are handled naturally.

Tensorial Deformation Measures for Flexible Joints

2010 ◽  
Vol 6 (3) ◽  
Author(s):  
Olivier A. Bauchau ◽  
Leihong Li ◽  
Pierangelo Masarati ◽  
Marco Morandini
Keyword(s):  
Finite Deformation ◽  
Nonlinear Behavior ◽  
Critical Issue ◽  
Finite Deformations ◽  
Flexible Joints ◽  
Elastic Bodies ◽  
Infinitesimal Deformations ◽  
Stiffness Characteristics ◽  
Definition Of

Flexible joints, sometimes called bushing elements or force elements, are found in all multibody dynamics codes. In their simplest form, flexible joints simply consist of sets of three linear and three torsional springs placed between two nodes of a multibody system. For infinitesimal deformations, the selection of the lumped spring constants is an easy task, which can be based on a numerical simulation of the joint or on experimental measurements. If the joint undergoes finite deformations, the identification of its stiffness characteristics is not so simple, especially if the joint itself is a complex system. When finite deformations occur, the definition of deformation measures becomes a critical issue. Indeed, for finite deformation, the observed nonlinear behavior of materials is partly due to material characteristics and partly due to kinematics. This paper focuses on the determination of the proper finite deformation measures for elastic bodies of finite dimension. In contrast, classical strain measures, such as the Green–Lagrange or Almansi strains, among many others, characterize finite deformations of infinitesimal elements of a body. It is argued that proper finite deformation measures must be of a tensorial nature, i.e., must present specific invariance characteristics. This requirement is satisfied if and only if the deformation measures are parallel to the eigenvector of the motion tensor.

A variational definition of the strain energy for an elastic string

1991 ◽  
Vol 25 (2) ◽  
pp. 137-148 ◽  
Author(s):  
Emilio Acerbi ◽  
Giuseppe Buttazzo ◽  
Danilo Percivale
Keyword(s):  
Strain Energy ◽  
Elastic String ◽  
Definition Of

scholarly journals The inverse non-stationary problem of identification of defects in an elastic rod

2021 ◽  
Vol 13 (S) ◽  
pp. 57-66
Author(s):  
Grigory V. FEDOTENKOV ◽  
Dmitry I. MAKAREVSKII ◽  
Yana A. VAHTEROVA ◽  
Trah Quyet THANG
Keyword(s):  
Solid Mechanics ◽  
Initial Conditions ◽  
Practical Interest ◽  
Stationary Problem ◽  
Technical Condition ◽  
Elastic Rod ◽  
Elastic Bodies ◽  
Fundamental Research ◽  
Great Practical Interest ◽  
Elastic Inclusions

Non-stationary inverse problems of deformed solid mechanics are among the most underexplored due to, inter alia, increasing dimension of non-stationary problems per unit as compared with stationary and static problems, as well as necessity to consider the initial conditions. In the context of the continuing progress of the aviation and aerospace industries, the question arises about technical condition monitoring of aircraft for the purposes of their safe operation. A large proportion of an aircraft structure consists of beam and rod elements exposed to various man-made and natural effects which cause defects inaccessible for visual inspection and required to be identified well in advance. It is well known that defects (such as cracks, cavities, rigid and elastic inclusions) are concentrators of stresses and largely cause processes, which lead to the destruction of elastic bodies. Therefore, the problem of identification of such defects and their parameters, i.e. the problem of identification, represents a great practical interest. Mathematically, the problem of identification represents a non-linear inverse problem. The development of methods of solving such problems is currently a live fundamental research issue.

Computational Elastic Rod Model Applied to DNA Looping

2007 ◽  
Author(s):  
Todd D. Lillian ◽  
N. C. Perkins ◽  
S. Goyal
Keyword(s):  
Strain Energy ◽  
Periodic Variation ◽  
Dna Looping ◽  
Cellular Functions ◽  
Elastic Rod ◽  
E Coli ◽  
Lactose Repressor ◽  
Rod Model ◽  
Elastic Rod Model ◽  
Multiple Boundary Conditions

DNA is a long flexible biopolymer containing genetic information. Proteins often take advantage of DNA’s inherent flexibility to perform their cellular functions. Here we present selected results from our computational studies of the mechanical looping of DNA by the Lactose repressor protein. The Lactose repressor resides in the bacterium E. coli and deforms DNA into a loop as a means of controlling the production of enzymes necessary for digesting lactose. We examine this looping process using a computational rod model [1–3] to understand the strain energy and geometry for the resultant DNA loops. Our model captures the multiple looped conformations of the molecule arising from both multiple boundary conditions and geometric nonlinearities. In addition, the model captures the periodic variation of strain energy with base-pair length as suggested by repression experiments (see, for example, [4, 5]).

Compliant Interface in Component Mode Synthesis

2020 ◽  
Author(s):  
Pierangelo Masarati ◽  
Fanny Darbas ◽  
Israël Wander
Keyword(s):  
Rigid Body ◽  
Structural Component ◽  
Strain Energy ◽  
Rigid Body Motion ◽  
Component Mode Synthesis ◽  
Body Motion ◽  
Structural Components ◽  
Definition Of ◽  
Flexible Models

Abstract Substructuring, or component mode synthesis, requires components to share interface regions. When components modeled with rather different, often incompatible levels of refinement need to be connected, correctly defining the interfaces may be important. This work proposes the definition of the reduction of interface regions to the equivalent rigid-body motion which minimizes the strain energy in the structural component. The proposed formulation provides a natural and physically sound solution for the connection of detailed structural components within coarse, multi-rigid-body and 1D flexible models.

scholarly journals From Electronegativity towards Reactivity—Searching for a Measure of Atomic Reactivity

Molecules ◽  
2021 ◽  
Vol 26 (12) ◽  
pp. 3680
Author(s):  
Sture Nordholm
Keyword(s):  
Conservation Laws ◽  
Strain Energy ◽  
Strain Relaxation ◽  
Ground States ◽  
Ionic Character ◽  
Bond Energies ◽  
Covalent Bonds ◽  
Ground State Degeneracy ◽  
The Stability ◽  
Definition Of

Pauling introduced the concept of electronegativity of an atom which has played an important role in understanding the polarity and ionic character of bonds between atoms. We set out to define a related concept of atomic reactivity in such a way that it can be quantified and used to predict the stability of covalent bonds in molecules. Guided by the early definition of electronegativity by Mulliken in terms of first ionization energies and Pauling in terms of bond energies, we propose corresponding definitions of atomic reactivity. The main goal of clearly distinguishing the inert gas atoms as nonreactive is fulfilled by three different proposed measures of atomic reactivity. The measure likely to be found most useful is based on the bond energies in atomic hydrides, which are related to atomic reactivities by a geometric average. The origin of the atomic reactivity is found in the symmetry of the atomic environment and related conservation laws which are also the origin of the shell structure of atoms and the periodic table. The reactive atoms are characterized by degenerate or nearly degenerate (several states of the same or nearly the same energy) ground states, while the inert atoms have nondegenerate ground states and no near-degeneracies. We show how to extend the use of the Aufbau model of atomic structure to qualitatively describe atomic reactivity in terms of ground state degeneracy. The symmetry and related conservation laws of atomic electron structures produce a strain (energy increase) in the structure, which we estimate by use of the Thomas-Fermi form of DFT implemented approximately with and without the symmetry and conservation constraints. This simplified and approximate analysis indicates that the total strain energy of an atom correlates strongly with the corresponding atomic reactivity measures but antibonding mechanisms prevent full conversion of strain relaxation to bonding.

scholarly journals AN INVESTIGATION INTO WORKING BEHAVIOR CHARACTERISTICS OF PARABOLIC CFST ARCHES APPLYING STRUCTURAL STRESSING STATE THEORY

2019 ◽  
Vol 25 (3) ◽  
pp. 215-227 ◽  
Author(s):  
Jun Shi ◽  
Kangkang Yang ◽  
Kaikai Zheng ◽  
Jiyang Shen ◽  
Guangchun Zhou ◽  
...  
Keyword(s):  
Structural Design ◽  
Strain Energy ◽  
Failure Load ◽  
Shape Function ◽  
Qualitative Change ◽  
State Theory ◽  
State Change ◽  
Strain Data ◽  
Definition Of ◽  
Behavior Characteristics

This paper conducts the experimental and simulative analysis of stressing state characteristics for parabolic concretefilled steel tubular (CFST) arches undergoing vertical loads. The measured stain data is firstly modeled as the generalized strain energy density (GSED) to describe structural stressing state mode. Then, the normalized GSED sum Ej,norm at each load Fj derives the Ej,norm-Fj curve reflecting the stressing state characteristics of CFST arches. Furthermore, the Mann-Kendall criterion is adopted to detect the stressing state change of the CFST arch during its load-bearing process, leading to the revelation of a vital stressing state leap characteristic according to the natural law from quantitative change to qualitative change of a system. The revealed qualitative leap characteristic updates the existing definition of the CFST arch’s failure load. Finally, the accurate formula is derived to predict the failure/ultimate loads of CFST arches. Besides, a method of numerical shape function is proposed to expand the limited strain data for further analysis of the stressing state submodes. The GSED-based analysis of structural stressing state opens a new way to recognize the unseen working behavior characteristics of arch structures and the updated failure load could contribute to the improvement on the structural design codes.

scholarly journals Simulating Crack Propagation of a Selected Structural Component of the PZL-130 Orlik TC-II Aircrafts

2014 ◽  
Vol 2014 (6) ◽  
pp. 119-127
Author(s):  
Krzysztof Jankowski ◽  
Piotr Reymer
Keyword(s):  
Crack Propagation ◽  
Mesh Generation ◽  
Structural Component ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Simulation Process ◽  
Proper Definition ◽  
Definition Of ◽  
Geometry Correction

Abstract This paper presents the process of estimating crack propagation within a selected structural component of the PZL-130 Orlik TC-II using a numerical model. The model is based on technical drawings and measurements of the real structure. The proper definition of the geometry, including the location and size of the gap between elements, is significant for mesh generation. During the simulation process the gap is combined node by node. Each time, the strain energy release rate (G) is calculated. The stress intensity factor and geometry correction factor are defined for consecutive crack lengths, and used further on to estimate crack propagation.

scholarly journals Buckling length of a frame member

2018 ◽  
Vol 51 (2) ◽  
pp. 49-61
Author(s):  
Teemu Tiainen ◽  
Markku Heinisuo
Keyword(s):  
Stiffness Matrix ◽  
Strain Energy ◽  
Integrated Design ◽  
Buckling Mode ◽  
Frame Design ◽  
Basic Task ◽  
Geometric Stiffness ◽  
Definition Of ◽  
Buckling Length ◽  
Frame Member

In steel frame design, the definition of buckling lengths of members is a basic task. Computers can be used to calculate the eigenmodes and corresponding eigenvalues for the frames and using these the buckling lengths of the members can be defined using Euler's equation. However, it is not always easy to say, which eigenmode should be used for the definition of the buckling length of a specific member. Conservatively, the lowest positive eigenvalue can be used for all members. In this paper, methods to define the buckling length of a specific member is presented. For this assessment, two ideas are considered. The first one uses geometric stiffness matrix locally and the other one uses strain energy measures to identify members taking part in a buckling mode. The behaviour of the methods is shown in several numerical examples. Both methods can be implemented into automated frame design, removing one big gap in the integrated design. This is essential when optimization of frames is considered.

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