Boundary Element Formulation for Thermal Stresses During Pulsed Laser Heating

2000 ◽  
Vol 68 (3) ◽  
pp. 480-489 ◽  
Author(s):  
P. H. Tehrani ◽  
L. G. Hector, ◽  
R. B. Hetnarski ◽  
M. R. Eslami
Keyword(s):  
Boundary Element ◽  
Thermal Stresses ◽  
Radiant Energy ◽  
Pulsed Laser ◽  
Heat Propagation ◽  
Thermomechanical Coupling ◽  
Stress Fields ◽  
Laser Resonator ◽  
Element Formulation ◽  
Anodized Aluminum

Pulsed lasers are used in a variety of materials processing applications that range from heating for metallurgical transformation to scribing vehicle identification numbers on anodized aluminum strips. These lasers are commonly configured to deliver a large quantity of heat energy in very short time intervals and over very small areas due to the manner in which radiant energy is stored within, and then released from, the laser resonator. At the present time, little is known about the effect of pulse duration on thermomechanical distortion during heating without phase change. To explore this issue, a boundary element method was developed to calculate temperature, displacement, and thermal stress fields in a layer that is rigidly bonded to an inert semi-space. The layer absorbs thermal energy from a repetitively pulsed laser in the plane of its free surface. The effects of two pulse durations, which differ by four-orders-of-magnitude, were examined in this work. The temporal profiles of ultrafast pulses of the order of ten picoseconds (such as those emitted by a mode-locked laser), and pulses of the order of tens-of-nanoseconds (such as those emitted by a Q-switched Nd:YAG laser) were mathematically modeled using a rectified sine function. The spatial profile of each pulse was shaped to approximate a Gaussian strip source. The equations of coupled thermoelasticity, wherein the speed of mechanical distortion due to material expansion during heat absorption is finite, but the speed of heat propagation within the layer is infinite, were solved for both pulse durations. The resulting temperature and stress fields were compared with those predicted in the limit of no thermomechanical coupling.

An improved boundary element formulation for calculating stress intensity factors: Application to aerospace structures

1987 ◽  
Vol 22 (4) ◽  
pp. 203-207 ◽  
Author(s):  
M H Aliabadi ◽  
D P Rooke ◽  
D J Cartwright
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Boundary Element ◽  
Stress Intensity Factors ◽  
Crack Tip ◽  
Stress Fields ◽  
Element Formulation ◽  
Intensity Factors ◽  
Singular Stress ◽  
Singular Stress Field

In order to compute stress intensity factors accurately, the standard boundary element method is modified to take explicit account of the singularity in the stresses at a crack-tip. The known expansion terms of the crack tip displacement and stress fields are subtracted to remove the numerical difficulties associated with the representation of a singular stress field at the crack-tip. Hence the accuracy of calculation is much improved, without appreciably increasing the amount of computation involved. Furthermore, the stress intensity factor is directly obtained as a part of a solution and no extrapolations are required. The improved formulation is applied to a configuration, which is representative of a part of the wing in a civil transport aeroplane. This configuration consists of a pair of circular cut-outs (supply ports) near to which smaller holes exist; these small holes are particularly susceptible to cracking.

scholarly journals Photogrammetric Process to Monitor Stress Fields Inside Structural Systems

Sensors ◽  
2021 ◽  
Vol 21 (12) ◽  
pp. 4023
Author(s):  
Leonardo M. Honório ◽  
Milena F. Pinto ◽  
Maicon J. Hillesheim ◽  
Francisco C. de Araújo ◽  
Alexandre B. Santos ◽  
...  
Keyword(s):  
Boundary Element ◽  
Real Time ◽  
Stress Fields ◽  
Structural Systems ◽  
Unknown Boundary ◽  
Stress Distributions ◽  
Displacement Fields ◽  
Time Stress ◽  
Beam Surface ◽  
Measured Displacement

This research employs displacement fields photogrammetrically captured on the surface of a solid or structure to estimate real-time stress distributions it undergoes during a given loading period. The displacement fields are determined based on a series of images taken from the solid surface while it experiences deformation. Image displacements are used to estimate the deformations in the plane of the beam surface, and Poisson’s Method is subsequently applied to reconstruct these surfaces, at a given time, by extracting triangular meshes from the corresponding points clouds. With the aid of the measured displacement fields, the Boundary Element Method (BEM) is considered to evaluate stress values throughout the solid. Herein, the unknown boundary forces must be additionally calculated. As the photogrammetrically reconstructed deformed surfaces may be defined by several million points, the boundary displacement values of boundary-element models having a convenient number of nodes are determined based on an optimized displacement surface that best fits the real measured data. The results showed the effectiveness and potential application of the proposed methodology in several tasks to determine real-time stress distributions in structures.

scholarly journals A new boundary element algorithm for modeling and simulation of nonlinear thermal stresses in micropolar FGA composites with temperature-dependent properties

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Mohamed Abdelsabour Fahmy
Keyword(s):  
Modeling And Simulation ◽  
Boundary Element ◽  
Thermal Stresses ◽  
Computation Time ◽  
Functionally Graded ◽  
Temperature Dependent ◽  
Time Step ◽  
Kirchhoff Transformation ◽  
Nonlinear Temperature ◽  
Temperature Dependent Properties

AbstractThe main aim of this article is to develop a new boundary element method (BEM) algorithm to model and simulate the nonlinear thermal stresses problems in micropolar functionally graded anisotropic (FGA) composites with temperature-dependent properties. Some inside points are chosen to treat the nonlinear terms and domain integrals. An integral formulation which is based on the use of Kirchhoff transformation is firstly used to simplify the transient heat conduction governing equation. Then, the residual nonlinear terms are carried out within the current formulation. The domain integrals can be effectively treated by applying the Cartesian transformation method (CTM). In the proposed BEM technique, the nonlinear temperature is computed on the boundary and some inside domain integral. Then, nonlinear displacement can be calculated at each time step. With the calculated temperature and displacement distributions, we can obtain the values of nonlinear thermal stresses. The efficiency of our proposed methodology has been improved by using the communication-avoiding versions of the Arnoldi (CA-Arnoldi) preconditioner for solving the resulting linear systems arising from the BEM to reduce the iterations number and computation time. The numerical outcomes establish the influence of temperature-dependent properties on the nonlinear temperature distribution, and investigate the effect of the functionally graded parameter on the nonlinear displacements and thermal stresses, through the micropolar FGA composites with temperature-dependent properties. These numerical outcomes also confirm the validity, precision and effectiveness of the proposed modeling and simulation methodology.

Reduced-Order Modeling of Unsteady Flows About Complex Configurations Using the Boundary Element Method

2002 ◽  
Vol 124 (4) ◽  
pp. 988-993 ◽  
Author(s):  
V. Esfahanian ◽  
M. Behbahani-nejad
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Reduced Order Modeling ◽  
Element Formulation ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Naca 0012 ◽  
Element Method

An approach to developing a general technique for constructing reduced-order models of unsteady flows about three-dimensional complex geometries is presented. The boundary element method along with the potential flow is used to analyze unsteady flows over two-dimensional airfoils, three-dimensional wings, and wing-body configurations. Eigenanalysis of unsteady flows over a NACA 0012 airfoil, a three-dimensional wing with the NACA 0012 section and a wing-body configuration is performed in time domain based on the unsteady boundary element formulation. Reduced-order models are constructed with and without the static correction. The numerical results demonstrate the accuracy and efficiency of the present method in reduced-order modeling of unsteady flows over complex configurations.

A boundary element formulation for a class of non-local damage models

1999 ◽  
Vol 36 (24) ◽  
pp. 3617-3638 ◽  
Author(s):  
R. García ◽  
J. Flórez-López ◽  
M. Cerrolaza
Keyword(s):  
Boundary Element ◽  
Element Formulation ◽  
Local Damage ◽  
Damage Models ◽  
Non Local

Theory of a Time Domain Boundary Element Development for the Dynamic Analysis of Coupled Multiphase Porous Media

2017 ◽  
Vol 08 (03n04) ◽  
pp. 1750007
Author(s):  
Pooneh Maghoul ◽  
Behrouz Gatmiri
Keyword(s):  
Boundary Element ◽  
Time Domain ◽  
Unsaturated Soils ◽  
Water Pressure ◽  
Domain Boundary ◽  
Fundamental Solutions ◽  
Element Formulation ◽  
Inertia Effects ◽  
Coupled Equations ◽  
The Time Domain

This paper presents an advanced formulation of the time-domain two-dimensional (2D) boundary element method (BEM) for an elastic, homogeneous unsaturated soil subjected to dynamic loadings. Unlike the usual time-domain BEM, the present formulation applies a convolution quadrature which requires only the Laplace-domain instead of the time-domain fundamental solutions. The coupled equations governing the dynamic behavior of unsaturated soils ignoring contributions of the inertia effects of the fluids (water and air) are derived based on the poromechanics theory within the framework of a suction-based mathematical model. In this formulation, the solid skeleton displacements [Formula: see text], water pressure [Formula: see text] and air pressure [Formula: see text] are presumed to be independent variables. The fundamental solutions in Laplace transformed-domain for such a dynamic [Formula: see text] theory have been obtained previously by authors. Then, the BE formulation in time is derived after regularization by partial integrations and time and spatial discretizations. Thereafter, the BE formulation is implemented in a 2D boundary element code (PORO-BEM) for the numerical solution. To verify the accuracy of this implementation, the displacement response obtained by the boundary element formulation is verified by comparison with the elastodynamics problem.

A Boundary Element Method for Multi-Body Contact Problems and its Application to the Analysis of a Huge Excavator

1995 ◽  
Author(s):  
Chong-De Liu ◽  
Jiyuan Yu ◽  
Xiaoming Wang
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Contact Problems ◽  
Fortran Program ◽  
Boundary Integral ◽  
Element Formulation ◽  
Body Contact ◽  
Boundary Integral Formulation ◽  
Discretization Technique ◽  
Multi Body

Abstract The derivation of a boundary integral formulation and discretization technique in terms of boundary elements for the solution of multi-body contact problems has been carried out. A FORTRAN program has been developed based on this boundary element formulation and has been applied to the stress analysis of a huge caterpillar excavator woth 16 m3 bucket capacity.

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