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Rocking block simulation based on numerical dissipation.

A M D'Altri1,2, G Vlachakis2, S de Miranda1

  • 1Department of Civil, Chemical, Environmental, and Materials Engineering, University of Bologna, Bologna, Italy.

Nonlinear Dynamics
|August 29, 2024
PubMed
Summary
This summary is machine-generated.

A new computational method accurately simulates rocking blocks using numerical dissipation without damping models. This approach enables rapid analysis of structural elements, crucial for heritage structures, with large time steps.

Keywords:
Cultural heritage structuresDynamicsFinite element methodMasonryOut-of-plane collapseRocking

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Area of Science:

  • Computational mechanics
  • Structural dynamics
  • Geotechnical engineering

Background:

  • Simulating the dynamic behavior of rocking blocks is essential for assessing the stability of structures, particularly historical ones.
  • Traditional methods often rely on damping models, which may not fully capture the complex dissipative phenomena during impacts.
  • Accurate and efficient computational tools are needed for analyzing rocking block responses under various loading conditions.

Purpose of the Study:

  • To propose a novel computational approach for simulating rocking blocks based on numerical dissipation.
  • To develop an accurate and efficient method for predicting the rocking dissipative phenomenon at impacts.
  • To establish a regression law for optimal time step selection in numerical simulations.

Main Methods:

  • Idealization of a rocking block as a solid body with contact-based formulation.
  • Employment of an implicit time integration scheme with optimized numerical dissipation.
  • Conducting a numerical campaign to derive an analytic regression law for time step setting.

Main Results:

  • The proposed numerical dissipation accurately predicts rocking dissipation without explicit damping models.
  • A validated regression law is established for time step selection, dependent on block geometry, stiffness, and restitution coefficient.
  • Simulations of rocking blocks relevant to structural engineering are achievable with large time steps (10⁻³ to 10⁻¹ s), ensuring computational efficiency.

Conclusions:

  • The numerical dissipation approach offers an effective and efficient method for simulating rocking blocks.
  • The derived regression law enhances the accuracy and reliability of time step selection in simulations.
  • This method shows significant promise for the analysis of cultural heritage structures and other critical engineering applications.