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Related Concept Videos

Unsymmetric Loading of Thin-Walled Members: Problem Solving01:07

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The shear center of a channel section with uniform thickness, height, and width, is determined by computing the shear force in the member and calculating the moments of inertia of the sections.
To compute the shear forces, find the shear flow at a specific distance from the endpoint using the vertical shear and the moment of inertia values. The total shear force on the flange is calculated by integrating the shear flow from one end of the flange to the other.
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Unsymmetric Loading of Thin-Walled Members01:23

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Thin-walled members with non-symmetrical cross-sections are vital to engineering structures, offering material efficiency and structural integrity. However, unsymmetrical loading on these members leads to complex stress distributions, resulting in simultaneous bending and twisting can cause deformation or structural failure. The interaction between bending and twisting requires detailed analysis to ensure structural resilience.
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When designing or analyzing a structural member, it is important to consider the internal loadings developed within the member. These internal loadings include normal force, shear force, and bending moment. Engineers can ensure that the structural member can support the applied external forces by calculating these internal loadings.
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The surrogate matrix methodology: A reference implementation for low-cost assembly in isogeometric analysis.

Daniel Drzisga1, Brendan Keith1, Barbara Wohlmuth1

  • 1Lehrstuhl für Numerische Mathematik, Fakultät für Mathematik (M2), Technische Universität München, Garching bei München, Germany.

Methodsx
|April 8, 2020
PubMed
Summary

This study introduces a new surrogate matrix method for isogeometric analysis (IGA). This approach significantly reduces computation time for IGA matrices with minimal impact on accuracy.

Keywords:
High orderIsogeometric analysisReference implementationSurrogate numerical methods

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Area of Science:

  • Computational mathematics
  • Numerical analysis
  • Scientific computing

Background:

  • Isogeometric analysis (IGA) typically requires computationally intensive element-scale quadrature for matrix computation.
  • Existing IGA methods face challenges in reducing the computational cost associated with matrix assembly.
  • There is a need for efficient approximations of matrices in IGA to reduce computational overhead.

Purpose of the Study:

  • To present a reference implementation of a novel surrogate matrix method for isogeometric analysis (IGA).
  • To demonstrate the effectiveness of this method in reducing computational cost.
  • To facilitate the adoption of this methodology in other IGA software libraries.

Main Methods:

  • Developed a surrogate matrix methodology that approximates matrices using quadrature on a subset of elements.
  • Implemented B-spline interpolation for computing the remaining matrix entries.
  • Integrated the surrogate matrix method into the open-source GeoPDEs IGA software library.

Main Results:

  • Successfully implemented the surrogate matrix methodology within the GeoPDEs software.
  • Validated the method by considering Poisson's problem.
  • Achieved significant reduction in matrix assembly time with negligible loss in solution accuracy.

Conclusions:

  • The surrogate matrix method offers a computationally efficient alternative for IGA matrix assembly.
  • The implementation in GeoPDEs demonstrates the practical applicability of the method.
  • This approach has the potential to accelerate IGA computations across various applications.