ISCM-10
Tenth Israel Symposium on Computational Mechanics
March 2001

ABSTRACTS


The Application of Genetic Algorithms for the Mechanical Characterization of the Tendon

Ariel Sverdlik and Yoram Lanir
Department of Biomedical Engineering
Technion - Israel Institute of Technology
32000 Haifa, ISRAEL

Abstract

Genetic Algorithms are search procedures based on evolution and genetics. They exploit previous ("historic") information in a randomized manner. The unknown variables are represented as genes on chromosomes. An initial population of chromosomes is randomly selected. Each chromosome is evaluated for its fitness by means of an optimization criterion. Based on their fitness, the chromosomes are randomly selected for mating, thus inducing genes swapping between mates, and creating a new generation of chromosomes. Mutation is introduced by random change in the "genes" (parameters values) within the chromosomes. The advantages of Genetic Algorithms are multifacet: they are intrinsically parallel and thus resistant to becoming trapped in local optima; they require no evaluation of gradients of the objective function; they are little affected by discontinuities, and, they perform well even in large scale and non-linear optimization problems. The main disadvantage of Genetic Algorithms is that they require extensive computer resources due to high number of fitness evaluations. In the present study a Genetic Algorithm was applied for estimation of material parameters of the tendon tissue.

The mechanical behavior of tendons is characterized by nonlinearity and by time dependence, as in most other soft tissues. The time-dependent aspects have two components: Viscoelasticity and Preconditioning. Preconditioning induces a decay in the stress level under cyclic tests and a concomitant increase in the reference (stress-free) length. Viscoelasticity and Preconditioning in tendons differ in their recovery characteristics: while recovery from viscoelastic effects is complete and has time constants in the range of seconds to minutes, preconditioning may be irreversible, and has time constants measured in hours to days.

Sheep digital extensor tendons were uni-axially stretched under a special loading protocol which separates the effects of time from those of the level of strain. The tendon specimens were tested in a chamber filled with physiological solution under constant temperature. The test and sampling protocols were computer controlled.

A morphologically based model was developed based on the observed non-uniform waviness of the numerous tendon fibers. The fibers tensile response includes viscoelasticity and preconditioning. The fibers' viscoelasticity was assumed to be quasi-linear, with a power law elastic response and an exponential reduced relaxation function. The preconditioning effects were assumed to result from elongation of the fibers which is expressed as an increase in the fiber's straightening strain. The resulting model for the entire tendon is highly non-linear and includes thirteen material parameters. The model's parameters were estimated to "best fit" the experimental data, using a Genetic Algorithm search. Conventional gradient-based search algorithms where generally unable to converge to optimal estimation, presumably due to both the model non-linear nature and the high number of parameters.

The Genetic Algorithm code used in the present study is the public domain GAOT, which is Matlab coded. Its reliability for the present study was tested with model-generated data to which random noise was added. It performed well in all cases.

The results of the study suggest that the time-dependent response of tendons have a reversible viscoelastic component and an irreversible preconditioning one. Preconditioning is manifested by stress decay, and a concomitant increase in the reference length. Theoretical/experimental analysis suggests that the complex response of the tendon can be integrated into a unified constitutive formulation, which accounts for viscoelasticity, preconditioning and morphology of the tendon's collagen fibers.

Scattering Analysis Techniques in a Focused Beam System

Reuven Shavit
Department of Electrical and Computer Engineering
Ben-Gurion University of the Negev
Beer Sheva, ISRAEL

Abstract

The scattering from an arbitrarily shaped cylinder is characterized by its Induced Field Ratio (IFR) and its co-polarized and cross-polarized scattering patterns. This talk describes how a unique focused beam measurement system is used to experimentally determine the scattering characteristics of an arbitrary shaped cylinder for normal and obliquely incident plane waves. The fields of the transmitting and receiving antennas of the focused beam measurement system are approximated by equivalent fundamental Gaussian beams. An analytical algorithm based on the computation of the coupling between the transmit and receive Gaussian beams of the focused beam measurement system and the scattered field of the cylinder, is used to determine the IFR and the co-polarized and cross-polarized scattering patterns of the cylinder. The experimental results obtained by this method for typical dielectric and metal cylinders agree well with the theoretical scattering characteristics computed numerically by the Method of Moments (MoM) and the Finite Element Method (FEM).

Ultra Wide Band Cylindrical Antenna Design Using the Green's Function Method (GFM) as an ABC and Far Field Operator in Genetic Optimization

R. Holtzman, Raphael Kastner, Ehud Heyman
Department of Electrical Engineering - Physical Electronics
Tel Aviv University
69978 Ramat Aviv, ISRAEL

Richard W. Ziolkowski
Department of Electrical and Computer Engineering
University of Arizona
Tucson, AZ 85721, USA

Abstract

The design procedure of an Ultra Wide Band (UWB) antenna, described herein, is based on genetic optimization far field parameters utilizing the FDTD as its mathematical model. Since the mathematical model is invoked repeatedly during the course of the optimization, an efficient implementation of the FDTD algorithm is of prime importance for this procedure to be effective. One of the main factors influencing the computation time is the size of the ``white space'' occupying the region between the antenna and the absorbing boundary. Since our target function is defined in the far field region, one may be tempted to extend the white space such that far field data will be included rather than to perform an independent integration at each iteration step, thereby increasing the computational burden. Alternatively, an efficient implementation of the FDTD should include an Absorbing Boundary Condition (ABC) that would perform adequately when placed in close proximity to the antenna, ideally conforming to the shape of the antenna as much as possible. To this end, we suggest the usage of the Green's Function Method (GFM) as the ABC in this work. The GFM can achieve the required properties by virtue of its unique capability of modeling arbitrarily shaped boundaries as well as arbitrary composition of the external domain. Moreover, the GFM is also used herein as a built-in integral operator leading to the far filed in a natural way at each iteration step. Results show the effectiveness of this method in generating new antenna structures taylored to specific needs.

A Numerical Absorbing Boundary Condition for Finite Element Analysis

Amir Boag
Department of Electrical Engineering - Physical Electronics
Tel Aviv University
69978 Ramat Aviv, ISRAEL

Abstract

The use of the Finite Element Method (FEM) for scattering and radiation problems requires one to couple, explicitly, the FEM computational domain to the unbounded free space external to the mesh region. To satisfy the radiation condition in the numerically rigorous sense, the FEM solution can either be matched to a modal expansion, or be combined with the MoM (also referred to as the Boundary Element Method). Both approaches lead to non-local boundary conditions that are exact, albeit at the expense of spoiling the sparsity of the matrices generated in these formulations. This has prompted many workers in FEM to search for an alternative, viz., to develop a local boundary condition which has relatively little effect on the sparsity of the FEM matrix. Notable contributions in this area have been made by a number of authors including Bayliss and Turkel, and Engquist and Majda. In a review paper describing the theoretical developments and the results of a comparative study of absorbing boundary conditions (ABCs) Mittra and Ramahi have shown that, for a circular outer boundary, the Bayliss-Turkel (B-T) ABC works well for lower-order cylindrical harmonics that are propagating in nature; however, the above ABC becomes inaccurate for the higher-order harmonics that are close to or beyond cutoff. Similarly, the Engquist-Majda (E-M) ABC does not absorb very well evanescent plane waves or plane waves incident upon the boundary at angles far from the normal to the boundary. Consequently, B-T and E-M ABCs require that the truncation boundary be removed far away from the outer boundary of the scatterer/antenna in order to diminish the evanescent content in the outgoing field impinging upon the boundary.

The objective of this paper is to address the problem of the systematic development of accurate and reliable, local type absorbing boundary conditions for the three-dimensional edge-based formulations of the FEM. The method followed here, is based upon the Numerical Absorbing Boundary Condition (NABC) concept. It begins by posing the problem of deriving the NABC as that of determining a numerical relationship that links the value of the field along a boundary edge to those at a selected number of neighboring edges. Here, we choose to link only parallel edges, making this version of the NABC similar to boundary conditions derived from scalar wave equation. While other options can be considered, this choice simplifies the geometrical considerations involved, while producing accurate results. The numerical relationship is derived by imposing the conditions that the equations must be satisfied to within a certain tolerance, by all of the outgoing wave components impinging upon the boundary from its interior. The number of adjacent boundary edges linked by the NABC is kept constant over the boundary, while the NABC coefficients are determined via a Singular Value Decomposition (SVD) based procedure. The number of edges involved in the NABC is determined first by using the criterion that the satisfaction of the outgoing field condition be at least as accurate as the satisfaction of the FEM equations at the internal edges (edges away from the boundary). The normalized error in the FEM equations for the interior edges is also used as a threshold in the SVD regularization of the equations for the NABC coefficients. Numerical examples that illustrate the derivation and application of the NABC will be presented.

A Simplified Method for Calculating Capacitance Matrix

Boris Roikhel, Yuval Yohai, and On Haran
Orbotech Ltd.

Abstract

An approximate integral equation method for the calculation of capacitance matrices is presented. The charge distribution is assumed to be uniform over the surface of each conductor. The method is applied to both 3D and 2D-models. The kernel of the integral equation is based on the Green's function either for the free space or for the boundary value problem. This method can be extended to more complicated charge distributions. Rigorous and approximate formulas are derived for several simple models in 3D and 2D. The final results are compared to ANSOFT_3D/2D simulations and other reference solutions. There is a good agreement between the results obtained by this method and those of ANSOFT_3D/2D simulations. In loss-less problems, the method can be used to compute the inductance from the calculated capacitance.

Indentation Fracture of Brittle Coating Layer

Herzl Chai
Department of Solid Mechanics, Materials, and Systems
Tel Aviv University
69978 Ramat Aviv, ISRAEL

Abstract

The role of a soft adhesive interlayer in determining critical conditions for fracture in brittle layer structures from indentation with hard spheres is investigated. A model transparent trilayer system consisting of a glass plate overlayer (thickness range 80 m to 2 mm) joined to a glass plate underlayer (thickness 5.6 mm) by an epoxy adhesive (thickness range 5 m to 8 mm), loaded at its top surface with a hard tungsten carbide sphere (radius 3.96 mm), facilitates in situ observations of the crack initiation and propagation. Whereas in bulk glass fracture occurs by inner Hertzian cone cracking immediately outside the contact circle, the soft adhesive allows the overlayer glass plate to flex, initiating additional transverse fracture modes within the overlayer: downward-extending outer ring cracks at the top glass surface well outside the contact, and upward-extending radial cracks at the bottom glass surface (i.e., at the glass/adhesive interface) on median planes containing the contact axis. The top and bottom surfaces of the glass overlayers are given selective pre-bonding abrasion treatments to ensure uniform flaw states, so as to enable accurate comparisons between crack initiation conditions. The adhesive bonding is sufficiently strong as to preclude delamination. Of the three transverse crack systems, the subsurface radials generate most easily in systems with larger adhesive thicknesses (and smaller overlayer thicknesses). Finite Element analysis of the indentation structure provides relations for the dependence of the critical loads for radial and ring cracking on adhesive as well as overlayer thicknesses, based on the assumption that crack initiation occurs when the maximum tensile stresses in the flexing glass plate exceed the bulk strength of the (abraded) glass. Coupled with the traditional "Auerbach's law" for cone crack initiation, these relations afford a basis for the construction of simple design diagrams for brittle layer systems joined by adhesives.

"Safe Life" Dynamic Component Life Extension Using a Damage Tolerance Approach

Moti Ben-Noon and Rotem Halevi
IAF

Avraham Berkovits
Faculty Of Aerospace Engineering
Technion - Israel Institute of Technology
32000 Haifa, ISRAEL

Abstract

Present practice in aircraft maintenance often requires mandatory replacement of dynamically loaded parts after a predefined number of flight hours. This "safe life" policy is often unnecessarily conservative, especially for costly and hard to replace parts. It is often possible to extend service life by using an on-condition replacement policy, coupled with an inspection schedule, instead of "safe life" replacement. An example of this policy, as applied to the pitch-housing component in the IAF AH-64A Apache fleet, is presented in this paper. Following a unique IAF usage spectrum survey, the manufacturer recommended reducing the life of the pitch-housing component from over 5000 flight hours to 600 hours. So far no pitch -housing removed form IAF aircraft exhibited fatigue cracks, although some have accumulated considerably more flight hours. Crack growth analysis of the pitch-housing lug conducted by the IAF, using NASTRAN/PATRAN, Stress-Check and NASA/FLAGROW software, showed that the component could be used safely for additional flight hours, by inspecting for cracks. If no crack is detected, the component can be used under an inspection policy that will ensure safe flight until a crack is detected. The influence of significantly large compressive loads on the stress distribution near a crack and the contribution of stresses induced by interference bushing to the total spectrum stresses were considered in this work. A final decision on implementing this life extension program on the IAF fleet awaits the results of laboratory tests under flight spectrum loading, and the development of adequate NDI techniques.

Dynamic Fracture Testing of Short Beam Specimens

Daniel Rittel
Faculty of Mechanical Engineering
Technion - Israel Institute of Technology
32000 Haifa, ISRAEL

Abstract

The need for testing small specimens is often dictated by the characteristic dimensions of the end product. While size limitations may influence quasi-static fracture testing, they definitely put constraints on dynamic fracture testing.

This talk presents our methodology and its application to the heavy alloys.

Dynamic fracture toughness is determined using a hybrid experimental-numerical approach. Within the framework of linear elastic fracture mechanics, the evolution of the stress intensity factor (SIF) is obtained by convolving the (experimental) applied load with the (calculated) specimen response to unit impulse force. The fracture toughness is defined as the value of the SIF at fracture time. The approach is validated by comparisons with analytical and independent experimental measurements of the crack-tip strains, to be described in this talk.

High Performance Computing for Computational Mechanics

Moshe Goldberg
HPC Support Group
Taub Computer Center
Technion - Israel Institute of Technology
32000 Haifa, ISRAEL

Tutorial Outline

  1. Introduction - High Performance Computing
  2. Architecture alternatives
  3. Message Passing
  4. "Shared-Memory" Parallel Programming
  5. Case Study


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Last modified: Mon Mar 26 15:44:53 "IST 2001