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Related Concept Videos

Scaling01:26

Scaling

In designing and analyzing filters, resonant circuits, or circuit analysis at large, working with standard element values like 1 ohm, 1 henry, or 1 farad can be convenient before scaling these values to more realistic figures. This approach is widely utilized by not employing realistic element values in numerous examples and problems; it simplifies mastering circuit analysis through convenient component values. The complexity of calculations is thereby reduced, with the understanding that...
Typical Model Studies01:30

Typical Model Studies

Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Design Example: Creating a Hydraulic Model of a Dam Spillway01:21

Design Example: Creating a Hydraulic Model of a Dam Spillway

Scaled hydraulic models of dam spillways provide a practical way to replicate and study the intricate flow dynamics of these structures. Often built to a 1:15 ratio, these models allow for observing critical water behavior, such as velocity distribution, flow patterns, and energy dissipation.
Modeling and Similitude01:12

Modeling and Similitude

Scaled modeling is a fundamental technique in engineering, enabling the study of large and complex systems by creating smaller, manageable replicas that recreate critical characteristics of the original. In hydrology and civil infrastructure, for example, scaled models of dams help analyze water flow, turbulence, and pressure. This method allows for accurate predictions of real-world behavior within a controlled environment, significantly reducing the cost and time involved in full-scale...

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Related Experiment Videos

Large Scale Parameter Estimation Problems in Frequency-Domain Elastodynamics Using an Error in Constitutive Equation

Biswanath Banerjee1, Timothy F Walsh, Wilkins Aquino

  • 1School of Civil and Environmental Engineering, Cornell University, Ithaca, New York, 14853 USA.

Computer Methods in Applied Mechanics and Engineering
|November 28, 2012
PubMed
Summary
This summary is machine-generated.

This study introduces an improved Error in Constitutive Equations (ECE) method for identifying material properties in elastodynamics. The enhanced Modified ECE (MECE) method uses a continuation scheme and parallel solvers for faster, large-scale material property reconstruction.

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Area of Science:

  • Solid Mechanics
  • Computational Mechanics
  • Materials Science

Background:

  • Inverse problems in elastodynamics require efficient methods for material property identification.
  • Existing Error in Constitutive Equations (ECE) methods face challenges in large-scale applications.
  • The Modified ECE (MECE) method incorporates measured data via a penalty term.

Purpose of the Study:

  • To develop and implement an efficient computational method for large-scale inverse identification of linear elastic material properties.
  • To accelerate the convergence of the MECE algorithm using a continuation scheme.
  • To enable the use of parallel finite element codes for solving MECE optimality conditions.

Main Methods:

  • Formulation and implementation of the Modified ECE (MECE) method.
  • Application of a continuation scheme for the penalty term in MECE.
  • Integration of a block successive over-relaxation (SOR) technique with parallel finite element solvers.

Main Results:

  • Successful reconstruction of spatial material property distribution from partial, noisy data.
  • Convergence acceleration by at least an order of magnitude using the continuation scheme.
  • Demonstration of computational efficiency on a 3D problem with ~400,000 unknown moduli.

Conclusions:

  • The proposed MECE method with continuation and SOR is computationally efficient for large-scale inverse material identification.
  • The approach significantly outperforms conventional L(2) minimization with quasi-Newton methods in terms of speed.
  • The methodology enables accurate material property reconstruction from limited and noisy measurements.