scholarly journals Reissner Plates with Plastic Behavior: Probability of Failure

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Ernesto Pineda-León ◽  
Alejandro Rodríguez-Castellanos ◽  
Dante Tolentino ◽  
José Manuel Rosales-Juárez ◽  
Ivan Felix-González ◽  
...  
Keyword(s):  
Boundary Integral Equations ◽  
Probability Of Failure ◽  
Boundary Integral ◽  
Three Dimensions ◽  
Initial Stresses ◽  
Plastic Behavior ◽  
Geometrical Properties ◽  
Incremental Method ◽  
Reissner’S Theory ◽  
Small Failure Probability

The current paper shows the application of the boundary element method for the analysis of plates under shear stress causing plasticity. In this case, the shear deformation of a plate is considered by means of Reissner’s theory. The probability of failure of a Reissner’s plate due to a proposed index plastic behavior IPB is calculated taking into account the uncertainty in mechanical and geometrical properties. The problem is developed in three dimensions. The classic plasticity’s theory is applied and a formulation for initial stresses that lead to the boundary integral equations due to plasticity is also used. For the plasticity calculation, the von Misses criterion is used. To solve the nonlinear equations, an incremental method is employed. The results show a relatively small failure probability (PF) for the ranges of loads between 0.6<W^<1.0. However, for values between 1.0<W^<2.5, the probability of failure increases significantly. Consequently, for W^≥2.5, the plate failure is imminent. The results are compared to those that were found in the literature and the agreement is good.

A Complex Variable Boundary Element-Free Method for Potential and Helmholtz Problems in Three Dimensions

2019 ◽  
Vol 17 (02) ◽  
pp. 1850129 ◽  
Author(s):  
Xiaolin Li ◽  
Shougui Zhang ◽  
Yan Wang ◽  
Hao Chen
Keyword(s):  
Boundary Element ◽  
Complex Variable ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Three Dimensions ◽  
Variable Boundary ◽  
Current Implementation ◽  
Element Free Method ◽  
Element Free ◽  
3D Surfaces

The complex variable boundary element-free method (CVBEFM) is a meshless method that takes the advantages of both boundary integral equations (BIEs) in dimension reduction and the complex variable moving least squares (CVMLS) approximation in element elimination. The CVBEFM is developed in this paper for solving 3D problems. This paper is an attempt in applying complex variable meshless methods to 3D problems. Formulations of the CVMLS approximation on 3D surfaces and the CVBEFM for 3D potential and Helmholtz problems are given. In the current implementation, the CVMLS shape function of 3D problems is formed with 1D basis functions, and the boundary conditions in the CVBEFM can be applied directly and easily. Some numerical examples are presented to demonstrate the method.

scholarly journals Magnetic micro-droplet in rotating field: numerical simulation and comparison with experiment

2017 ◽  
Vol 821 ◽  
pp. 266-295 ◽  
Author(s):  
J. Erdmanis ◽  
G. Kitenbergs ◽  
R. Perzynski ◽  
A. Cēbers
Keyword(s):  
Magnetic Field ◽  
Boundary Integral Equations ◽  
Three Dimensional ◽  
Dipolar Interaction ◽  
Boundary Integral ◽  
Rotating Magnetic Field ◽  
Three Dimensions ◽  
Triaxial Ellipsoid ◽  
Equilibrium Shapes ◽  
Magnetic Droplet

Magnetic droplets obtained by induced phase separation in a magnetic colloid show a large variety of shapes when exposed to an external field. However, the description of the shapes is often limited. Here, we formulate an algorithm based on three-dimensional boundary-integral equations for strongly magnetic droplets in a high-frequency rotating magnetic field, allowing us to find their figures of equilibrium in three dimensions. The algorithm is justified by a series of comparisons with known analytical results. We compare the calculated equilibrium shapes with experimental observations and find a good agreement. The main features of these observations are the oblate–prolate transition, the flattening of prolate shapes with the increase of magnetic field strength and the formation of starfish-like equilibrium shapes. We show both numerically and in experiments that the magnetic droplet behaviour may be described with a triaxial ellipsoid approximation. Directions for further research are mentioned, including the dipolar interaction contribution to the surface tension of the magnetic droplets, accounting for the large viscosity contrast between the magnetic droplet and the surrounding fluid.

Fast direct solvers for integral equations in complex three-dimensional domains

Acta Numerica ◽  
2009 ◽  
Vol 18 ◽  
pp. 243-275 ◽  
Author(s):  
Leslie Greengard ◽  
Denis Gueyffier ◽  
Per-Gunnar Martinsson ◽  
Vladimir Rokhlin
Keyword(s):  
Integral Equations ◽  
Degrees Of Freedom ◽  
Boundary Integral Equations ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Three Dimensions ◽  
Computer Hardware ◽  
Matrix Vector Multiplication ◽  
Gradient Type ◽  
Mathematical Foundations

Methods for the solution of boundary integral equations have changed significantly during the last two decades. This is due, in part, to improvements in computer hardware, but more importantly, to the development of fast algorithms which scale linearly or nearly linearly with the number of degrees of freedom required. These methods are typically iterative, based on coupling fast matrix-vector multiplication routines with conjugate-gradient-type schemes. Here, we discuss methods that are currently under development for the fast, direct solution of boundary integral equations in three dimensions. After reviewing the mathematical foundations of such schemes, we illustrate their performance with some numerical examples, and discuss the potential impact of the overall approach in a variety of settings.

Hypersingular Boundary Integral Equations: Some Applications in Acoustic and Elastic Wave Scattering

1990 ◽  
Vol 57 (2) ◽  
pp. 404-414 ◽  
Author(s):  
G. Krishnasamy ◽  
L. W. Schmerr ◽  
T. J. Rudolphi ◽  
F. J. Rizzo
Keyword(s):  
Boundary Integral Equations ◽  
Acoustic Scattering ◽  
Boundary Integral ◽  
Three Dimensions ◽  
Finite Part ◽  
Important Special Case ◽  
Hypersingular Integrals ◽  
Hadamard Finite Part ◽  
Spatial Dimensions ◽  
Regular Line

The properties of hypersingular integrals, which arise when the gradient of conventional boundary integrals is taken, are discussed. Interpretation in terms of Hadamard finite-part integrals, even for integrals in three dimensions, is given, and this concept is compared with the Cauchy Principal Value, which, by itself, is insufficient to render meaning to the hypersingular integrals. It is shown that the finite-part integrals may be avoided, if desired, by conversion to regular line and surface integrals through a novel use of Stokes’ theorem. Motivation for this work is given in the context of scattering of time-harmonic waves by cracks. Static crack analysis of linear elastic fracture mechanics is included as an important special case in the zero-frequency limit. A numerical example is given for the problem of acoustic scattering by a rigid screen in three spatial dimensions.

scholarly journals Total Incremental Method for Solving Nonlinear System of Equation Due to Plasticity of Reissner Plates with Boundary Element Method

2017 ◽  
Vol 8 (1) ◽  
Author(s):  
Supriyono Supriyono
Keyword(s):  
Nonlinear System ◽  
Boundary Integral Equations ◽  
Plastic Material ◽  
Boundary Integral ◽  
System Equation ◽  
Incremental Method ◽  
Perfectly Plastic ◽  
A Cell ◽  
Elastic Perfectly Plastic ◽  
Von Mises

In this paper a total incremental method for solving nonlinear system equation due to plasticity of shear deformable plates is presented. The material is assumed to undergo small strains. The von Mises criterion is used to evaluate the plastic zone and elastic perfectly plastic material behaviour is assumed. An initial stress formulation is used to formulate the boundary integral equations. The domain integral due to material nonlinearity is evaluated using a cell discretization technique. Several examples are presented and comparisons are made to demonstrate the validity and the accuracy of the total incremental method to solve the nonlinear system of equation due to plasticity.

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