r4.05.07 Nonlinear soil-structure interaction with the Laplace-Temps method

Summary:

This document is a theoretical note describing the Laplace-Temps method (cf. [U2.06.05]) developed in the CALC_MISS operator (cf. [U7.03.12]) for the result type “FICHIER_TEMPS”. It is part of the framework of non-linear soil-structure interaction calculations (ISS) based on Code_Aster - MISS3D chaining.

The principle of solving such a non-linear calculation is based on a substructuring technique where two sub-domains are generally considered: on the one hand, a non-linear bounded domain corresponding essentially to the structure part (and possibly, the ground surrounding the foundation) and on the other hand, an unbounded soil domain with elastic linear behavior. This domain decomposition makes it possible to apply the finite element method (Code_Aster) for the transient modeling of the non-linear problem and a boundary element method (MISS3D) for the calculation of the impedance matrix representing the dynamic behavior in time of the semi-infinite ground domain.

In this context, the Laplace-Temps method makes it possible to calculate the time impedance operator from a particular sampling of the complex frequency space (Laplace domain). In particular, this sampling is based on the polynomial characteristic of a second-order linear multi-step method. Likewise, the Laplace-Temps method makes it possible to evaluate, at each moment of the seismic calculation, of the convolutional integral translating the soil-structure interaction efforts of the coupled system.

• 1. Introduction
  • 1.1. Problem: evaluation of convolutional integrals
• 2. The Laplace-Temps method
  • 2.1. General principle
  • 2.2. Application to ground impedance operators
• 3. Calculation of impedance in time
  • 3.1. Implementation in code_aster
  • 3.2. Key numerical considerations
• 4. Seismic analysis
  • 4.1. Calculation of the seismic force in time
  • 4.2. Time integration diagram
• 5. Bibliography