Patch Element Model for the Evaluation of Displacement Fields Within an Elastic Solid from a Non-Contact Immersion Transducer: Application to the 2004 Ultrasonic Benchmark Problem

2005 ◽  
Author(s):  
C. V. Krishnamurthy
Keyword(s):  
Elastic Solid ◽  
Element Model ◽  
Benchmark Problem ◽  
Displacement Fields ◽  
Transducer Application

Penetration of a Half Space by a Rectangular Cylinder

1979 ◽  
Vol 46 (3) ◽  
pp. 587-591 ◽  
Author(s):  
A. Cemal Eringen ◽  
F. Balta
Keyword(s):  
Half Space ◽  
Stress Singularity ◽  
Elastic Solid ◽  
Interatomic Interaction ◽  
Elastic Half Space ◽  
Rigid Block ◽  
Field Equations ◽  
Displacement Fields ◽  
Rectangular Cylinder ◽  
Stress And Displacement Fields

The stress and displacement fields are determined in an elastic half space loaded by a rectangular frictionless, rigid block normally at its surface. The semi-infinite solid is considered to be an elastic solid with nonlocal interatomic interaction. The field equations of the nonlocal elasticity and boundary conditions are employed to treat this contact problem. Interestingly the classical stress singularity at the edges of the block are not present in the nonlocal solutions. Consequently the critical applied load for the initiation of penetration of the rigid cylinder into the semi-infinite solid can be determined without recourse to any criterion foreign to the theory. The stress field obtained is valid even for penetrators of submicroscopic width.

scholarly journals Identification of Local Elastic Parameters in Heterogeneous Materials Using a Parallelized Femu Method

2019 ◽  
Vol 24 (4) ◽  
pp. 140-156
Author(s):  
L. Petureau ◽  
P. Doumalin ◽  
F. Bremand
Keyword(s):  
Genetic Algorithm ◽  
Model Updating ◽  
Heterogeneous Materials ◽  
Element Model ◽  
Finite Element Model Updating ◽  
Elastic Parameters ◽  
Displacement Fields ◽  
Quadratic Error ◽  
Strain Fields ◽  
Computation Cost

Abstract In this work, we explore the possibilities of the widespread Finite Element Model Updating method (FEMU) in order to identify the local elastic mechanical properties in heterogeneous materials. The objective function is defined as a quadratic error of the discrepancy between measured fields and simulated ones. We compare two different formulations of the function, one based on the displacement fields and one based on the strain fields. We use a genetic algorithm in order to minimize these functions. We prove that the strain functional associated with the genetic algorithm is the best combination. We then improve the implementation of the method by parallelizing the algorithm in order to reduce the computation cost. We validate the approach with simulated cases in 2D.

The Stress Field Caused by a Circular Cylindrical Inclusion in a Transversely Isotropic Elastic Solid

2003 ◽  
Vol 70 (6) ◽  
pp. 825-831 ◽  
Author(s):  
H. Hasegawa ◽  
M. Kisaki
Keyword(s):  
Stress Field ◽  
Strain Energy ◽  
Elastic Solid ◽  
Transversely Isotropic ◽  
Cylindrical Inclusion ◽  
Stress Distributions ◽  
Axisymmetric Stress ◽  
Displacement Fields ◽  
Isotropic Solid ◽  
Stress And Displacement Fields

Exact solutions are presented in closed form for the axisymmetric stress and displacement fields caused by a circular solid cylindrical inclusion with uniform eigenstrain in a transversely isotropic elastic solid. This is an extension of a previous paper for an isotropic elastic solid to a transversely isotropic solid. The strain energy is also shown. The method of Green’s functions is used. The numerical results for stress distributions are compared with those for an isotropic elastic solid.

Numerical analysis of a time domain elastoacoustic problem

2019 ◽  
Vol 40 (2) ◽  
pp. 1122-1153
Author(s):  
Rodolfo Araya ◽  
Rodolfo Rodríguez ◽  
Pablo Venegas
Keyword(s):  
Numerical Analysis ◽  
Error Estimates ◽  
Elastic Solid ◽  
Coupled System ◽  
Optimal Error Estimates ◽  
Finite Difference Schemes ◽  
Displacement Fields ◽  
Weak Formulation ◽  
Fully Discrete ◽  
Optimal Rate Of Convergence

Abstract This paper deals with the numerical analysis of a system of second order in time partial differential equations modeling the vibrations of a coupled system that consists of an elastic solid in contact with an inviscid compressible fluid. We analyze a weak formulation with the unknowns in both media being the respective displacement fields. For its numerical approximation, we propose first a semidiscrete in space discretization based on standard Lagrangian elements in the solid and Raviart–Thomas elements in the fluid. We establish its well-posedness and derive error estimates in appropriate norms for the proposed scheme. In particular, we obtain an $\mathrm L^{\infty }(\mathrm L^2)$ optimal rate of convergence under minimal regularity assumptions of the solution, which are proved to hold for appropriate data of the problem. Then we consider a fully discrete approximation based on a family of implicit finite difference schemes in time, from which we obtain optimal error estimates for sufficiently smooth solutions. Finally, we report some numerical results, which allow us to assess the performance of the method. These results also show that the numerical solution is not polluted by spurious modes as is the case with other alternative approaches.

Stress and Strain Fields in the Hemispherical Head of an FCC Regenerator During the Lifting Maneuver in Cyclone Replacement

2013 ◽  
Author(s):  
Erik Garrido ◽  
Euro Casanova
Keyword(s):  
Oil And Gas ◽  
Oil And Gas Industry ◽  
Element Model ◽  
Sensitivity Analyses ◽  
Mechanical Equipment ◽  
Displacement Fields ◽  
Gas Industry ◽  
Total Displacement ◽  
Stress And Displacement Fields ◽  
Special Studies

The Oil and Gas industry is constantly seeking for improvements in the design of mechanical equipment. Each refining process is the subject of continuous research, which is frequently addressed in the revisions of the corresponding standard. Nevertheless, particular technologies such as the Fluid Catalytic Cracking Units (FCCU) are not governed by any International Standard but by designs developed and patented by specialized licensors. The implementation of new designs requires special studies of the original equipment in order to assess the feasibility of the related works and the required provisions to accomplish the revamp. This work studies the stress and displacement fields occurring in the hemispherical head of an FCC regenerator during the lifting maneuver for a typical cyclone replacement. A parametric finite element model was developed and stress and total displacement charts are presented as a function of diameters and thicknesses of hemispherical heads commonly found in the industry. Sensitivity analyses are presented with respect to a variation of ±15% of the applied loads and the size of the plenum chamber. Therefore, the results shown in this work present a reference framework for the replacement of cyclones in FCC regenerators when removing their hemispherical heads.

Additional Separated-Variable Solutions of the Biharmonic Equation in Polar Coordinates

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
I. H. Stampouloglou ◽  
E. E. Theotokoglou
Keyword(s):  
Fourth Order ◽  
Biharmonic Equation ◽  
Direct Determination ◽  
Additional Term ◽  
Elastic Solid ◽  
Polar Coordinates ◽  
Polar Coordinate System ◽  
Radial Coordinate ◽  
Displacement Fields ◽  
Polar Coordinate

From the biharmonic equation of the plane problem in the polar coordinate system and taking into account the variable-separable form of the partial solutions, a homogeneous ordinary differential equation (ODE) of the fourth order is deduced. Our study is based on the investigation of the behavior of the coefficients of the above fourth order ODE, which are functions of the radial coordinate r. According to the proposed investigation additional terms, φ¯−m(r,θ)(1≤m≤n) other than the usually tabulated in the Michell solution (1899, “On the Direct Determination of Stress in an Elastic Solid, With Application to the Theory of Plates,” Proc. Lond. Math. Soc., 31, pp. 100–124) are found. Finally the stress and the displacement fields due to each one additional term of φ¯−m(r,θ) are determined.

Thermal stress analysis of plates and shallow shells by hybrid finite-element method

1974 ◽  
Vol 9 (3) ◽  
pp. 152-158
Author(s):  
B Tabarrok ◽  
V S Hoa
Keyword(s):  
Finite Element ◽  
Thermal Stress ◽  
Stress Analysis ◽  
Element Model ◽  
Displacement Fields ◽  
Shallow Shells ◽  
Thermal Stress Analysis ◽  
Hybrid Finite Element Method ◽  
Variational Functional ◽  
Hybrid Finite Element

A rectangular finite-element model has been developed for thermal-stress analysis of shallow shells. The elemental equations are obtained from a two-field variational principle which employs equilibriating stress fields within the elements and compatible displacement fields along inter-element boundaries. The extremization of the variational functional tends to satisfy the compatibility requirements within the elements and equilibrium conditions along inter-element boundaries. The element is employed for thermal-stress analysis of several examples and the numerical results obtained are compared with some analytical results.

Strain-based health indicators for the structural health monitoring of stiffened composite panels

2020 ◽  
pp. 1045389X2092482
Author(s):  
Dimitrios P Milanoski ◽  
Theodoros H Loutas
Keyword(s):  
Structural Health Monitoring ◽  
Health Monitoring ◽  
Mechanical Load ◽  
Elastic Solid ◽  
Health Indicators ◽  
Element Model ◽  
Health State ◽  
Structural Health ◽  
Stiffened Composite Panels ◽  
Stiffened Structures

A common defect of composite-stiffened structures is the disbond at the interface between the two constituents (skin/stringer), as a result of inefficient manufacturing process or foreign object impacts in service. Generally, discontinuities within the volume of an elastic solid medium, subjected to mechanical load, cause anomalies on the strain field in the near vicinity of the discontinuity. Utilizing this observation, this work investigates the effect of artificially induced disbonds in the skin/stiffener interface of an aeronautical-grade generic element. A structural health monitoring methodology is developed, leveraging on numerically simulated strains along the stringer foot which aims to assess the health state of the panel as the size of the disbonds increases. The study is implemented using a parametric finite element model generating various disbond scenarios. Longitudinal strain values are acquired at the exact points where in reality actual fiber Bragg grating sensors will be located. Two types of commonly utilized strain-based health indicators are evaluated, and their drawbacks are revealed and discussed. A new health indicator is proposed that proves its capability to monitor growing disbonds while being both load- and baseline-independent.

Special Elements for Composites Containing Hexagonal and Circular Fibers

2015 ◽  
Vol 12 (04) ◽  
pp. 1540012 ◽  
Author(s):  
Qing H. Qin ◽  
H. Wang
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Weak Form ◽  
Element Model ◽  
Fundamental Solutions ◽  
Hybrid Functional ◽  
Displacement Fields ◽  
Hybrid Finite Element ◽  
Representative Unit Cell ◽  
Square Array

In this paper, unidirectional fiber reinforced composites with periodic square array of circular and hexagonal fibers is studied by a novel fundamental-solution-based hybrid finite element model. Due to the periodicity of composites, a representative unit cell containing a single fiber with circular or hexagonal cross section is taken into consideration and analyzed using the proposed hybrid finite element model. In the present numerical model, special polygonal fiber elements with arbitrary number of sides are developed by coupling the independent element interior and frame displacement fields. The element interior displacement fields are approximated by the combination of fundamental solutions to prior satisfy the governing equation of the problem, so that the domain integral appeared in the weak-form hybrid functional in terms of dual variables is converted into boundary integrals. Independently the element frame displacement fields are approximated by the conventional shape functions to guarantee the continuity of adjacent elements. Following this, special polygonal fiber elements are constructed to reduce mesh effort in the fiber region and achieve good accuracy with fewer elements. Finally, numerical tests are carried out for assessing the performance of the present special elements.

A Finite-Element Model for Plane-Strain Plasticity

1979 ◽  
Vol 46 (3) ◽  
pp. 536-542 ◽  
Author(s):  
P. G. Hodge ◽  
H. M. van Rij
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Plane Strain ◽  
Element Model ◽  
Displacement Fields ◽  
Model Based ◽  
Strain Plasticity ◽  
Continuous Displacement ◽  
Basic Equations ◽  
Punch Problem

A finite-element model is proposed which allows for both straining within each element and slip between two elements. Basic equations are derived and are shown to almost completely uncouple into two constituent components: the conventional finite-element equations for continuous displacement fields and the “slip” equations which were recently derived for a model based on slipping of rigid triangles. The model is applied to the Prandtl punch problem and is shown to combine the best features of its two constituents.

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