INVERSE SQUARE ROOT MOMENT SINGULARITIES IN RECTANGULAR PLATES CONTAINING AN INTERNAL LINE SUPPORT

2009 ◽  
Vol 06 (01) ◽  
pp. 1-21 ◽  
Author(s):  
YOS SOMPORNJAROENSUK ◽  
KRAIWOOD KIATTIKOMOL
Keyword(s):  
Strain Energy ◽  
Integral Transform ◽  
Internal Line ◽  
Square Root ◽  
Rectangular Plates ◽  
Bending Moments ◽  
Partial Support ◽  
Uniform Loading ◽  
Dual Series Equations ◽  
Standard Techniques

Two cases of a rectangular plate having moment singularities at the ends of a partial internal line support are analytically investigated. The bending of the plate by uniform loading is formulated in terms of dual-series equations. Application of the finite Hankel integral transform reduces the dual-series equations to a Fredholm integral equation of the second kind that can be solved by standard techniques. Numerical results are given for the deflections and bending moments along the line outside of an internal line support and the change in strain energy due to the presence of a partial support.

scholarly journals Dual-series equations formulation for static deformation of plates with a partial internal line support

2007 ◽  
Vol 34 (3) ◽  
pp. 221-248 ◽  
Author(s):  
Yos Sompornjaroensuk ◽  
Kraiwood Kiattikomol
Keyword(s):  
Integral Equation ◽  
Fredholm Integral Equation ◽  
Hankel Transform ◽  
Internal Line ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Distributed Load ◽  
Dual Series Equations ◽  
Finite Hankel Transform ◽  
Standard Techniques

The paper deals with the application of dual-series equations to the problem of rectangular plates having at least two parallel simply supported edges and a partial internal line support located at the centre where the length of internal line support can be varied symmetrically, loaded with a uniformly distributed load. By choosing the proper finite Hankel transform, the dual-series equations can be reduced to the form of a Fredholm integral equation which can be solved conveniently by using standard techniques. The solutions of integral equation and the deformations for each case of the plates are given and discussed in details.

A characteristic type of instability in the large deflexions of elastic plates III. Curved rectangular plates in axial compression

1954 ◽  
Vol 222 (1148) ◽  
pp. 44-59 ◽  
Keyword(s):  
Axial Compression ◽  
Rectangular Plates ◽  
Bending Moments ◽  
Elastic Plates ◽  
Characteristic Type ◽  
Circular Tubes ◽  
Axis Parallel ◽  
Post Buckling ◽  
Thin Walled ◽  
The Stability

The analysis of part I is extended to deal with the case of free-edged rectangular plates having an initial curvature about an axis parallel to one pair of opposite edges and loaded by distributed bending moments applied to the straight edges and compressive forces applied to the curved edges. In particular, the stability and post-buckling behaviour of such plates subjected to the compressive forces alone is studied. The axially symmetrical buckling of thin-walled circular tubes in axial compression is also considered. Experimental plates are found to buckle at loads rather lower than those predicted.

Pure Moment Testing for Spinal Biomechanics Applications: Fixed Versus 3D Floating Ring Cable-Driven Test Designs

2012 ◽  
Author(s):  
Jessica A. Tang ◽  
Justin K. Scheer ◽  
Christopher P. Ames ◽  
Jenni M. Buckley
Keyword(s):  
Spinal Column ◽  
Bending Moments ◽  
Pure Bending ◽  
Uniform Loading ◽  
Flexion Extension ◽  
Driven System ◽  
Accepted Standard ◽  
Pure Moment ◽  
Bending Modes ◽  
Biomechanical Tests

For spine biomechanical tests, the cable-driven system in particular has been widely used to apply pure bending moments. The advantages to pure moment testing lie in its consistency as an accepted standard protocol across previous literature and its ability to ensure uniform loading across all levels of the spinal column. Of the methods used for pure moment testing, cable-driven set-ups are popular due to their low requirements and simple design. Crawford et al [1] were the first to employ this method, but prior work by our group indicated a discrepancy between applied and intended moment for this system in flexion-extension only [2]. We hypothesize that this discrepancy can be observed in other bending modes and minimized with a second-generation floating ring design to eliminate off-axis loads.

A Benchmark Study of Bending Limit Load Finite Element Analysis for Locally Wall Thinned Pipes

2013 ◽  
Author(s):  
Phuong H. Hoang ◽  
Bostjan Bezensek ◽  
Howard J. Rathbun
Keyword(s):  
Finite Element ◽  
Limit Load ◽  
Benchmark Problems ◽  
Square Root ◽  
Bending Moments ◽  
Finite Element Analyses ◽  
Element Analysis ◽  
Benchmark Analysis ◽  
Benchmark Study ◽  
Computer Codes

Finite element analyses (FEA) have been used to study the effects of multi-axial loadings on bending limit load of local wall thinned pipes. It has been shown by investigators that torsion can be combined with bending moments using SRSS (Square Root of the Sum of the Squares) method for planar flaws with a limited axial extent. The treatment of torsion for non-planar flaws, which exceed the axial extent limit, will be a subject for future investigations. Since the reported FEA results are for various pipe sizes, flaw shapes with different mesh sizes, element types and computer codes, a set of benchmark problems was proposed and analyzed by participating investigators. The benchmark analysis results are presented in this paper.

Reliability Based Deep Water Spool Piece Design

2013 ◽  
Author(s):  
Naresh Juluri ◽  
Elie Dib ◽  
Sherif el-Gebaly ◽  
Philip Cooper
Keyword(s):  
Monte Carlo Simulation ◽  
High Pressure ◽  
Monte Carlo ◽  
Deep Water ◽  
Square Root ◽  
Bending Moments ◽  
Industry Practice ◽  
Fabrication Tolerances ◽  
Outside Diameter ◽  
A Current

Long spools are often required to absorb the end expansion of deep water high pressure and high temperature flowlines. These spools typically have significant metrology and fabrication tolerances. Metrology and spool fabrication tolerances lead to misalignments at the connector hub face. Residual loads then arise from spool deformation due to the installation forces that are required to match-up the connector faces. It is a current industry practice to design the spools for multiple independent tolerances at extreme limits in all directions. Previous project experience shows that the Algebraic Sum (AS) combination of multiple independent tolerances at extreme limits may result in large spools where the probability of occurrence of these tolerances at extreme limits is quite low. The use of less conservative SRSS (square root of sum of squares) combination has been suggested in this paper as an alternative to the Algebraic Sum combination. Due to the large number of misalignment components, the probability of exceeding the loads in the spool and at the connector obtained by the SRSS method is small and is within the applicable failure probabilities defined in DNV-OS-F101. The SRSS method is demonstrated in this paper by using a Monte Carlo simulation. Five different spools have been analysed to demonstrate the suitability of using SRSS misalignments when the spools are designed to DNV-OS-F101. The spools considered include 10″, 16″ and 20″ outside diameter spools to represent different sizes at different loading combinations. Maximum bending moments in the spool and maximum moments at the connector have been considered to check the SRSS feasibility. The results indicate that it is acceptable to use SRSS misalignments as an alternative to AS misalignments. Considering SRSS misalignments in preference to AS leads to reduced spool size and reduced loadings on connectors.

ANALYTICAL AND FINITE ELEMENT MODELING AND SIMULATION OF BUCKLING AND POSTBUCKLING OF DELAMINATED ORTHOTROPIC PLATES

2011 ◽  
Vol 02 (01) ◽  
pp. 97-104 ◽  
Author(s):  
LALITHA CHATTOPADHYAY ◽  
S. SRIDHARA MURTHY
Keyword(s):  
Finite Element ◽  
Strain Energy ◽  
Failure Modes ◽  
Integral Transform ◽  
Laminated Composite ◽  
Strain Energy Release ◽  
Orthotropic Plates ◽  
Manufacturing Defects ◽  
Laminated Composite Materials ◽  
Plane Compression

Delamination is one of the most common failure modes of laminated composite materials, and can be caused by manufacturing defects or impact loading. Under compression, a delaminated composite plate may buckle and tend to enlarge the delaminated area, which can lead to loss of global structural stability. This paper presents the elastic buckling and postbuckling analysis of an axially loaded beam-plate with an across-the-width delamination, located at a given depth below the upper surface of the plate. The analysis is done by considering a layered orthotropic plate containing through-width delamination, subjected to in-plane compression. The problem is analyzed by two approaches: (i) A simple analytical model for determining strain energy release rate is obtained using integral transform approach; (ii) A finite element representation of the problem is modeled and analyzed using MSC/NASTRAN and the buckling load is calculated.

Rectangular Plates on Unilateral Edge Supports: Part 1—Theory and Numerical Analysis

1986 ◽  
Vol 53 (1) ◽  
pp. 146-150 ◽  
Author(s):  
J. P. Dempsey ◽  
Hui Li
Keyword(s):  
Singular Integral Equations ◽  
Integral Transforms ◽  
Rectangular Plates ◽  
Centrally Symmetric ◽  
Solution Methods ◽  
Dual Series Equations ◽  
Finite Integral ◽  
Loss Of Contact ◽  
Laterally Loaded ◽  
Numerical Approaches

The corners of a simply supported, laterally loaded rectangular plate must be anchored to prevent them from lifting off the supports. If no such anchors are provided, and the supports are unilateral or capable of exerting forces in one direction only, parts of the plate will bend away from the supports upon loading. The loss of contact when uplift of laterally loaded rectangular plates is not prevented is examined in this paper. Arbitrary centrally symmetric loading is considered. Finite integral transforms convert the coupled dual-series equations that result from the Levy-Nadai approach to two coupled singular integral equations. Different solution methods are applicable for sagged and unsagged supports; these two numerical approaches are discussed in detail.

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