Numerical Methods for the Limit Analysis of Plates

1968 ◽  
Vol 35 (4) ◽  
pp. 796-802 ◽  
Author(s):  
P. G. Hodge ◽  
T. Belytschko
Keyword(s):  
Finite Element ◽  
Numerical Methods ◽  
Mathematical Programming ◽  
Rectangular Plate ◽  
Yield Point ◽  
Lower Bounds ◽  
Limit Analysis ◽  
Upper And Lower Bounds ◽  
Mathematical Programming Problems

The determination of upper and lower bounds on the yield-point loads of plates are formulated as mathematical programming problems by using finite element representations for the velocity and moment fields. Results are presented for a variety of square and rectangular plate problems and are compared to other available solutions.

scholarly journals RESIDUAL DISPLACEMENTS‘ PROGRESIVE ANALYSIS OF THE MULTISUPPORTED BEAM / DAUGIAATRAMĖS SIJOS LIEKAMŲJŲ POSLINKIŲ PROGRESINĖ ANALIZĖ

2014 ◽  
Vol 6 (5) ◽  
pp. 461-467 ◽  
Author(s):  
Liudas Liepa ◽  
Agnė Gervytė ◽  
Ela Jarmolajeva ◽  
Juozas Atkočiūnas
Keyword(s):  
Numerical Methods ◽  
Mathematical Models ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Analysis Problem ◽  
Residual Displacements ◽  
Repeated Load ◽  
Energy Principles

This paper focuses on a shakedown behaviour of the ideally elasto-plastic beams system under variable repeated load. The mathematical models of the analysis problems are created using numerical methods, extremum energy principles and mathematic programming. It is shown that during the shakedown process the residual displacements vary non-monotonically. By solving analysis problem, where the load locus is being progressively expanded, it is possible to determine the upper and lower bounds of residual displacements. Suggested methods are ilustrated by solving multisupported beam example problem. The results are obtained considering principle of the small displacements. Nagrinėjamas idealiai tampriai plastinės lenkiamos strypinės sistemos prisitaikomumo būvis, veikiant kartotinei kintamajai apkrovai. Analizės uždavinių matematiniai modeliai sudaromi, pasitelkus skaitinius metodus, ekstreminius energinius principus ir matematinį programavimą. Parodoma, kad prisitaikant konstrukcijai jos liekamieji poslinkiai gali kisti nemonotoniškai. Išsprendus analizės uždavinį, kuriame progresyviai plečiama apkrovos veikimo sritis, galima nustatyti viršutines ir apatines liekamųjų poslinkių kitimo ribas. Siūloma metodika iliustruota daugiaatramės sijos liekamųjų poslinkių skaičiavimo pavyzdžiu. Rezultatai gauti, esant mažų poslinkių prielaidai.

Pipe Whip—Bounding the Required Restraint Capacity

1985 ◽  
Vol 107 (4) ◽  
pp. 356-360
Author(s):  
R. Peek
Keyword(s):  
Finite Element ◽  
Energy Balance ◽  
Lower Bounds ◽  
Finite Element Methods ◽  
Plastic Hinge ◽  
Upper And Lower Bounds ◽  
Trial And Error ◽  
Rigid Plastic ◽  
Numerical Example ◽  
Plastic Pipe

Energy balance methods commonly in use for the design of pipe whip restraints are based on the solution for the motion of a rigid-plastic pipe before impact against the restraint, with the assumption that after impact, the whipping portion of the pipe continues to rotate about the plastic hinge location determined for conditions before impact. Such energy balance methods are not necessarily conservative because: 1) the plastic hinge which forms in the pipe moves after impact on the restraint; and 2) elastic pipe deformations are not considered. Here, upper and lower bounds to the required restraint capacity are derived. In contrast to finite element methods, which are very time-consuming, the upper and lower bounds can be evaluated by simple hand calculations. Another advantage is that the required restraint capacity is calculated directly. No trial and error design is required. A numerical example shows that for a typical pipe and restraint, the upper and lower bounds differ by as little as 20 percent.

Deformation and Stiffness of Spur Gearing Solved by FEM

2014 ◽  
Vol 611 ◽  
pp. 194-197 ◽  
Author(s):  
Miroslav Malák
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Methods ◽  
Computer Technology ◽  
Spur Gears ◽  
Gear Teeth ◽  
Element Method

Gear teeth are deformed due to the load. Recently, at ever faster evolving computer technology and the available literature, we can encounter modern numerical methods, such as finite element method (FEM), which can serve as methods for the determination of deflection gearing. This paper deals with stiffness and deformation of teeth of spur gears solution by finite element method.

scholarly journals Bounds for the Collapse Load of a Beam Compressed by Three Dies

1956 ◽  
Vol 9 (4) ◽  
pp. 419
Author(s):  
W Freiberger
Keyword(s):  
Plastic Deformation ◽  
Plastic Flow ◽  
Lower Bounds ◽  
Limit Analysis ◽  
Velocity Fields ◽  
The Other ◽  
Upper And Lower Bounds ◽  
Collapse Load ◽  
Plastic Yielding ◽  
Plane Plastic

This paper deals with the problem of the plastic deformation of a beam under the action of three perfectly rough rigid dies, two dies applied to one side, one die to the other side of the beam, the single die being situated between the two others. It is treated as a problem of plane plastic flow. Discontinuous stress and velocity fields are assumed and upper and lower bounds for the pressure sufficient to cause pronounced plastic yielding determined by limit analysis.

scholarly journals Ramsey numbers for certain k-graphs

1981 ◽  
Vol 30 (3) ◽  
pp. 284-296 ◽  
Author(s):  
Stefan A. Burr ◽  
Richard A. Duke
Keyword(s):  
Lower Bounds ◽  
Complete Solution ◽  
Ramsey Number ◽  
Upper And Lower Bounds ◽  
Uniform Hypergraph ◽  
Steiner Systems ◽  
Ramsey Numbers ◽  
Existence Question

AbstractWe are interested here in the Ramsey number r(T, C), where C is a complete k-uniform hypergraph and T is a “tree-like” k-graph. Upper and lower bounds are found for these numbers which lead, in some cases, to the exact value for r(T, C) and to a generalization of a theorem of Chváta1 on Ramsey numbers for graphs. In other cases we show that a determination of the exact values of r(T, C) would be equivalent to obtaining a complete solution to existence question for a certain class of Steiner systems.

Determination of the Buckling Load for Columns of Variable Stiffness

1949 ◽  
Vol 16 (4) ◽  
pp. 406-410
Author(s):  
C. C. Miesse
Keyword(s):  
Lower Bounds ◽  
Axial Loading ◽  
Variable Stiffness ◽  
Buckling Load ◽  
Upper And Lower Bounds ◽  
Variable Section ◽  
Rayleigh Principle

Abstract A method is given for determining both upper and lower bounds on the critical or buckling load for variable-section columns with axial loading. This method, which is an extension of the Rayleigh principle, is illustrated by three examples.

A Posteriori Error Estimator for a Weak Galerkin Finite Element Solution of the Stokes Problem

2017 ◽  
Vol 7 (3) ◽  
pp. 508-529 ◽  
Author(s):  
Xiaobo Zheng ◽  
Xiaoping Xie
Keyword(s):  
Finite Element ◽  
Lower Bounds ◽  
Stokes Problem ◽  
Three Dimensions ◽  
Upper And Lower Bounds ◽  
Error Estimator ◽  
A Posteriori ◽  
Weak Galerkin ◽  
Galerkin Finite Element ◽  
Velocity Approximation

AbstractA robust residual-based a posteriori error estimator is proposed for a weak Galerkin finite element method for the Stokes problem in two and three dimensions. The estimator consists of two terms, where the first term characterises the difference between the L2-projection of the velocity approximation on the element interfaces and the corresponding numerical trace, and the second is related to the jump of the velocity approximation between the adjacent elements. We show that the estimator is reliable and efficient through two estimates of global upper and global lower bounds, up to two data oscillation terms caused by the source term and the nonhomogeneous Dirichlet boundary condition. The estimator is also robust in the sense that the constant factors in the upper and lower bounds are independent of the viscosity coefficient. Numerical results are provided to verify the theoretical results.

Fundamental Frequency of Simply Supported Rectangular Plates With Linearly Varying Thickness

1965 ◽  
Vol 32 (1) ◽  
pp. 163-168 ◽  
Author(s):  
F. C. Appl ◽  
N. R. Byers
Keyword(s):  
Rectangular Plate ◽  
Fundamental Frequency ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Varying Thickness

Upper and lower bounds for the fundamental eigenvalue (frequency) of a simply supported rectangular plate with linearly varying thickness are given for several taper ratios and plan geometries. These bounds were determined using a previously published method which yields convergent bounds. In the present study, all results have been obtained to within 0.5 percent maximum possible error.

Sign in / Sign up

Export Citation Format

Share Document