The buckling mode extracted from the LDLT-decomposed large-order stiffness matrix

2002 ◽  
Vol 18 (7) ◽  
pp. 459-467 ◽  
Author(s):  
Fumio Fujii ◽  
Hirohisa Noguchi
Keyword(s):  
Stiffness Matrix ◽  
Buckling Mode ◽  
Large Order

Effect of In-Plane Fiber Tow Waviness Upon the Tensile Strength Characteristics of Fiber Reinforced Composites of Carbon/Epoxy AS4/3501-6

2015 ◽  
Author(s):  
Sai Bhargav Pottavathri ◽  
Rajeev Nair ◽  
Ramazan Asmatulu
Keyword(s):  
Stiffness Matrix ◽  
High Stress ◽  
Local Stress ◽  
Longitudinal Direction ◽  
Stress Concentrations ◽  
Molding Process ◽  
Buckling Mode ◽  
Severity Factor ◽  
Fiber Waviness ◽  
Mechanical Methods

The purpose of this study was to investigate the strength and effectiveness when induced with ‘in-plane fiber tow waviness’ in a composite ply of carbon/epoxy AS4/3501-6. Fiber waviness is usually induced by infusion processes and inherent in fabric architectures. Composite structural details like ply drops and ply joints can cause serious fiber misalignment. These are usually dependent on parameters such as ply thickness, percentage of plies dropped, and mold geometry and pressure, and pressure of the resin which slides the dry fibers during the resin transfer molding process. Fiber disorientation due to fiber tow waviness in ‘in-plane’ direction has been the subject of recent studies on wind turbine blade materials and other aerospace laminates with reports of compression strengths and failure strains that are borderline, depending upon the reinforcement architecture, matrix resin and environment. Waviness is expected to reduce compressive strength due to two primary factors. The fibers may be oriented in such a way that the geometry that results because of the orientation may exacerbate the basic fiber, strand, or layer buckling mode of failure. The waviness could also shift the fiber orientation of the axis of the ply longitudinal direction which eventually results in matrix dominated failures for plies normally orientated in the primary load direction (0°). Both global and local stress & strain values generated by the finite element model were validated by the traditional mechanical methods using ply/local stiffness matrix and global/reduced stiffness matrix. A precise geometry of waviness on different materials was modeled with different wave severity factor and a parametric study was conducted. Three different defects were modeled where the angle of misalignment ranged from 5 to 15 degrees with wavelength ranging from 1 inch to 1.5 inches and amplitude ranging from 0.03 inches to 0.7 inches. This revealed the effect of ‘in-plane fiber tow waviness’ on the stress distribution and loss of strength in carbon/epoxy AS4/3501-6. The results clearly show that the effect of ‘in-plane fiber tow waviness’ leads to resin rich areas which causes high stress concentrations and decrease in the strength ratio, ultimately leading to delamination’s.

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.

The Russian ruble crisis of December 2014

2016 ◽  
pp. 66-86
Author(s):  
A. Obizhaeva
Keyword(s):  
Microstructure Analysis ◽  
Future Market ◽  
Effective Response ◽  
Large Order ◽  
Short Period ◽  
The Face ◽  
Front Running ◽  
Futures And Options

The paper presents a microstructure analysis of the crash of the Russian ruble in mid-December 2014. The author shows that the market break probably happened due to the execution of a large order that converted Russian rubles into U.S. dollars over a short period of a few days. Expirations of futures and options as well as possible front-running could have exacerbated the collapse of the Russian currency. The paper discusses measures taken by the Moscow Exchange and Bank of Russia during the episode and makes several recommendations to prevent a repetition of the similar events and provide an effective response in the face of future market breaks.

Computational issues for two multiple constraint stiffness matrix adjustment methods

1995 ◽  
Author(s):  
Kyle Dippery ◽  
Suzanne Smith ◽  
Zhaojun Bai
Keyword(s):  
Stiffness Matrix ◽  
Multiple Constraint

A Computer-Aided System for Automatic Mitosis Detection from Breast Cancer Histological Slide Images based on Stiffness Matrix and Feature Fusion

2015 ◽  
Vol 10 (4) ◽  
pp. 476-493 ◽  
Author(s):  
Ashkan Tashk ◽  
Mohammad Sadegh Helfroush ◽  
Habibollah Danyali ◽  
Mojgan Akbarzadeh
Keyword(s):  
Breast Cancer ◽  
Stiffness Matrix ◽  
Feature Fusion ◽  
Mitosis Detection ◽  
Computer Aided ◽  
Histological Slide

Physical Ultrasonics of Composites

2011 ◽  
Author(s):  
Dale Chimenti ◽  
Stanislav Rokhlin ◽  
Peter Nagy
Keyword(s):  
Composite Laminates ◽  
Stiffness Matrix ◽  
Composite Plates ◽  
Anisotropic Media ◽  
Anisotropic Materials ◽  
Ultrasonic Waves ◽  
Laminated Plates ◽  
Structure Characteristic ◽  
Major Advance

Physical Ultrasonics of Composites is a rigorous introduction to the characterization of composite materials by means of ultrasonic waves. Composites are treated here not simply as uniform media, but as inhomogeneous layered anisotropic media with internal structure characteristic of composite laminates. The objective here is to concentrate on exposing the singular behavior of ultrasonic waves as they interact with layered, anisotropic materials, materials which incorporate those structural elements typical of composite laminates. This book provides a synergistic description of both modeling and experimental methods in addressing wave propagation phenomena and composite property measurements. After a brief review of basic composite mechanics, a thorough treatment of ultrasonics in anisotropic media is presented, along with composite characterization methods. The interaction of ultrasonic waves at interfaces of anisotropic materials is discussed, as are guided waves in composite plates and rods. Waves in layered media are developed from the standpoint of the "Stiffness Matrix", a major advance over the conventional, potentially unstable Transfer Matrix approach. Laminated plates are treated both with the stiffness matrix and using Floquet analysis. The important influence on the received electronic signals in ultrasonic materials characterization from transducer geometry and placement are carefully exposed in a dedicated chapter. Ultrasonic wave interactions are especially susceptible to such influences because ultrasonic transducers are seldom more than a dozen or so wavelengths in diameter. The book ends with a chapter devoted to the emerging field of air-coupled ultrasonics. This new technology has come of age with the development of purpose-built transducers and electronics and is finding ever wider applications, particularly in the characterization of composite laminates.

Consistent co-rotational framework for Euler-Bernoulli and Timoshenko beam-column elements under distributed member loads

2021 ◽  
pp. 136943322098663
Author(s):  
Yi-Qun Tang ◽  
Wen-Feng Chen ◽  
Yao-Peng Liu ◽  
Siu-Lai Chan
Keyword(s):  
Coordinate System ◽  
Stiffness Matrix ◽  
Traditional Method ◽  
Local Coordinate System ◽  
Frame Structures ◽  
Global Coordinate System ◽  
Single Element ◽  
Geometrically Nonlinear ◽  
Geometrically Nonlinear Analysis ◽  
Geometric Stiffness

Conventional co-rotational formulations for geometrically nonlinear analysis are based on the assumption that the finite element is only subjected to nodal loads and as a result, they are not accurate for the elements under distributed member loads. The magnitude and direction of member loads are treated as constant in the global coordinate system, but they are essentially varying in the local coordinate system for the element undergoing a large rigid body rotation, leading to the change of nodal moments at element ends. Thus, there is a need to improve the co-rotational formulations to allow for the effect. This paper proposes a new consistent co-rotational formulation for both Euler-Bernoulli and Timoshenko two-dimensional beam-column elements subjected to distributed member loads. It is found that the equivalent nodal moments are affected by the element geometric change and consequently contribute to a part of geometric stiffness matrix. From this study, the results of both eigenvalue buckling and second-order direct analyses will be significantly improved. Several examples are used to verify the proposed formulation with comparison of the traditional method, which demonstrate the accuracy and reliability of the proposed method in buckling analysis of frame structures under distributed member loads using a single element per member.

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