Subramaniam D. Rajan

A shape optimization approach based on natural design variables and shape functions

Abstract The general problem of concern is to find the optimum shape of an elastic body, which requires minimizing an objective function subject to stress, displacement, frequency, and manufacturing constraints. The basic approach so far has been to choose a set of geometric design variables that define the shape of the structure. Typically the design variables have been chosen as coefficients of splines and polynomials, coordinates of ‘control’ nodes, and other geometric parameters. An automatic finite element discretization scheme that uses geometric entities such as lines, arcs, splines, and blending functions, is then used to relate changes in position of interior grid points in the finite element mesh to changes in the design variables. In this paper, a set of natural design variables is chosen as the design variables defining the shape. Specifically, the design variables are the magnitudes of a set of fictitious loads applied on the structure. The displacements produced by these fictitious loads, or natural shape functions, are added onto the initial mesh to obtain the new shape. Consequently, a linear relationship is established between changes in grid point locations and design variables through a finite element analysis. Plane elasticity problems are solved using the new approach. The quality of the finite element meshes produced and other salient features of the shape optimal design problem are discussed.

Perturbative inversion methods for obtaining bottom geoacoustic parameters in shallow water

Three perturbative inverse methods for obtaining bottom geoacoustic parameters as a function of depth in shallow water are described. The required input data are the trapped mode eigenvalues for one or more frequencies, the group velocity dispersion curves for one or more modes, or the cw pressure field versus range. In each case, a Fredholm integral equation arises that can be solved using linear inverse theory, and for which resolution and variance estimates of the solution can be readily made. Attention is focused primarily on the modal eigenvalue inverse problem for which the theory for determining the compressional wave speed, compressional wave attenuation, and density is developed in detail. Properties of this technique are studied using synthetic data and include investigations of the dependence of the results on acoustic frequency, number of modes excited, and partial a priori knowledge of the bottom. The method is demonstrated on experimental data obtained in Nantucket Sound at 140 and 220 Hz. D...

A comparison of broadband and narrow‐band modal inversions for bottom geoacoustic properties at a site near Corpus Christi, Texas

Detailed comparison between narrow-band and broadband techniques used in a series of acoustic experiments are presented with emphasis on (a) comparisons of the pressure field versus range predicted, (b) comparisons of the bottom compressional-wave-speed model generated, (c) the variance of the bottom model estimated, and (d) the resolution of the bottom model generated. The range dependence of the bottom medium and the seasonal dependence of the near-surface sediment sound-speed profile are observed and discussed

Shape optimal design using fictitious loads

Implementation aspects of the natural velocity field approach for shape optimal design are discussed. The problem of concern is to find the optimum shape of an elastic body that requires minimizing an objective function subject to stress, displacement, frequency, and manufacturing constraints. In this paper, fictitious loads are applied at certain control nodes on an auxiliary structure, and the deformation produced by these loads is used to update the shape. The use of beam stiffeners in the auxiliary structure leads to smoother shapes, Furthermore, softer material properties in the auxiliary structure result in faster convergence when iterating through the feasibile region. The method is applied in conjunction with both discrete and continuum methods of design sensitivity analysis

Long-term changes in the material properties of brain tissue at the implant–tissue interface

OBJECTIVE Brain tissue undergoes dramatic molecular and cellular remodeling at the implant-tissue interface that evolves over a period of weeks after implantation. The biomechanical impact of such remodeling on the interface remains unknown. In this study, we aim to assess the changes in the mechanical properties of the brain-electrode interface after chronic implantation of a microelectrode. APPROACH Microelectrodes were implanted in the rodent cortex at a depth of 1 mm for different durations-1 day (n = 4), 10-14 days (n = 4), 4 weeks (n = 4) and 6-8 weeks (n = 7). After the initial duration of implantation, the microelectrodes were moved an additional 1 mm downward at a constant speed of 10 µm s(-1). Forces experienced by the microelectrode were measured during movement and after termination of movement. The biomechanical properties of the interfacial brain tissue were assessed from measured force-displacement curves using two separate models-a two-parameter Mooney-Rivlin hyperelastic model and a viscoelastic model with a second-order Prony series. MAIN RESULTS Estimated shear moduli using a second-order viscoelastic model increased from 0.5-2.6 kPa (day 1 of implantation) to 25.7-59.3 kPa (after 4 weeks of implantation) and subsequently decreased to 0.8-7.9 kPa after 6-8 weeks of implantation in 6 of the 7 animals. The estimated elastic modulus increased from 4.1-7.8 kPa on the day of implantation to 24-44.9 kPa after 4 weeks. The elastic modulus was estimated to be 6.8-33.3 kPa in 6 of the 7 animals after 6-8 weeks of implantation. The above estimates suggest that the brain tissue surrounding the microelectrode evolves from a stiff matrix with maximal shear and elastic modulus after 4 weeks of implantation into a composite of two different layers with different mechanical properties-a stiff compact inner layer surrounded by softer brain tissue that is biomechanically similar to brain tissue-during the first week of implantation. Tissue micromotion-induced stresses on the microelectrode constituted 12-55% of the steady-state stresses on the microelectrode on the day of implantation (n = 4), 2-21% of the steady-state stresses after 4 weeks of implantation (n = 4), and 4-10% of the steady-state stresses after 6-8 weeks of implantation (n = 7). SIGNIFICANCE Understanding biomechanical behavior at the brain-microelectrode interface is necessary for the long-term success of implantable neuroprosthetics and microelectrode arrays. Such quantitative physical characterization of the dynamic changes in the electrode-tissue interface will (a) drive the design and development of more mechanically optimal, chronic brain implants, and (b) lead to new insights into key cellular and molecular events such as neuronal adhesion, migration and function in the immediate vicinity of the brain implant.

Determination of compressional wave speed profiles using modal inverse techniques in a range‐dependent environment in Nantucket Sound

An inverse method for determining geoacoustic properties in a horizontally stratified, shallow‐water waveguide is extended to the case of a weakly range‐dependent environment [Frisk et al., J. Acoust. Soc. Am. 86, 1928–1939 (1989)]. The technique consists of estimating the local modal eigenvalues from the beam‐formed output of a horizontal array and using these data as input to modal inverse methods for obtaining the local bottom parameters. Specifically, the approach is applied to data at 140 and 220 Hz obtained in a shallow‐water environment with a known abrupt change in bathymetry. First, a range‐independent medium is assumed and both iteration of forward models and perturbative inversion methods are applied to the modal data to obtain estimates of the bottom sound velocity profile. Although the perturbative inversion results are clearly superior, neither approach reproduces the full dependence with range of the observed pressure fields or the complete modal peak structure. In particular, the data exhi...

Characterization of Dynamic Tensile Testing Using Aluminum Alloy 6061-T6 at Intermediate Strain Rates

Dynamic tensile tests are conducted on aluminum alloy (AA) 6061-T6 using a high-speed servohydraulic machine at intermediate strain rates to validate the testing technique and to investigate the strain-rate effect on the material’s stress-strain behavior and failure mode. We present the experimental procedures and results discussing the constitutive response of the alloy at strain rates up to approximately 200  s-1. The predominant frequencies of the high-speed testing machine were characterized by modal analysis, and we analyzed the effect from vibration of the system and loading rate on flow stress by using a single degree-of-freedom (SDOF) spring-mass-damper model. We tested two different specimen sizes at a wide range of actuator velocities to achieve the desired strain rates. Results show that the yield strength, ultimate strength, and failure strain were dependent on strain rate. We fitted the data to the Johnson-Cook (JC) constitutive model, and the resulting parameters are comparable to published ...

Optimal placement of critical speeds in rotor-bearing systems

The design of a rotor-bearing system is an iterative process in which the parameters that influence the design are modified until the desired design objectives are achieved. Primary among the design objectives is the minimization of the response amplitude within the operating range of the rotor system. An automated design procedure for the optimal placement of the critical speeds of a rotor is presented. The desired design objective is cast as a nonlinear programming problem that minimizes an objective function subject to constraints. The optimization program interacts with an analysis program to search for the feasible optimal design.

The Kauai Experiment

The Kauai Experiment was conducted from June 24 to July 9, 2003 to provide a comprehensive study of acoustic propagation in the 8–50 kHz band for diverse applications. Particular sub‐projects were incorporated in the overall experiment 1) to study the basic propagation physics of forward‐scattered high‐frequency (HF) signals including time/angle variability, 2) to relate environmental conditions to underwater acoustic modem performance including a variety of modulation schemes such as MFSK, DSSS, QAM, passive‐phase conjugation, 3) to demonstrate HF acoustic tomography using Pacific Missile Range Facility assets and show the value of assimilating tomographic data in an ocean circulation model, and 4) to examine the possibility of improving multibeam accuracy using tomographic data. To achieve these goals, extensive environmental and acoustic measurements were made yielding over 2 terabytes of data showing both the short scale (seconds) and long scale (diurnal) variations. Interestingly, the area turned out...

Evaluation of high‐resolution frequency estimation methods for determining frequencies of eigenmodes in shallow water acoustic field

In shallow water, the acoustic field in the far field, due to a point source, can be modeled as a sum of contributions from trapped modes propagating in the wave guide. In many applications, it is necessary to estimate the eigenvalues of these modes from a measurement of the acoustic field made on a horizontal array using a monochromatic source. In this paper the performance of two high‐resolution methods (MUSIC and ESPRIT) in estimating the eigenvalues of the modes from the measured field is evaluated. In particular, we investigate the ability of these methods to estimate the frequencies accurately for various signal to noise ratios and their ability to resolve closely spaced frequencies using synthetic noisy data. Of the two methods, ESPRIT had the better performance in terms of the variance of the estimates. Simulation performed to study the effect of modeling errors on the performance of the algorithms showed that, for a medium that is weakly range dependent, the performance of the algorithms is not a...