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Application of discrete shape function in absolute nodal coordinate formulation.

Zhicheng Song1, Jinbao Chen1, Chuanzhi Chen1

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Summary

This study simplifies applying the absolute nodal coordinate method to arbitrary-section beams using invariant matrix and Gerstmayr methods. These techniques enhance the efficiency of solving elastic forces and force Jacobians in beam analysis.

Keywords:
absolute nodal coordinate formulation (ANCF)discrete shape functioninvariant matricestensor of stress

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Area of Science:

  • Mechanical Engineering
  • Computational Mechanics
  • Structural Analysis

Background:

  • The absolute nodal coordinate method (ANCM) is a powerful tool for flexible multibody dynamics.
  • Applying ANCM to arbitrary-section beams presents computational challenges due to complex integral calculations.
  • Standard Euler-Bernoulli beam theory simplifies analysis for symmetrical cross-sections.

Purpose of the Study:

  • To develop and validate methods for solving integrals within the ANCM for arbitrary-section beams.
  • To demonstrate the applicability of ANCM to beams with non-uniform cross-sections.
  • To enhance the computational efficiency of ANCM for beam structures.

Main Methods:

  • Utilizing the invariant matrix method and the Gerstmayr method for single integral evaluation.
  • Employing discrete function interpolation to incorporate arbitrary cross-section characteristics.
  • Applying Gaussian integration to accelerate the computation of elastic forces and force Jacobians.

Main Results:

  • The proposed single integral methods successfully extend ANCM to arbitrary-section beams.
  • Simplifications arise for Euler-Bernoulli beams due to their symmetrical and small cross-sections.
  • Gaussian integration significantly improves the efficiency of solving elastic force and force Jacobian.

Conclusions:

  • The invariant matrix and Gerstmayr methods provide effective solutions for ANCM integrals in arbitrary-section beams.
  • The study validates the adaptability of ANCM for complex beam geometries.
  • Enhanced computational efficiency is achieved through optimized integration techniques.