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3 results

A Primer on Theoretical Soil Mechanics
  • Dimitrios Kolymbas
  • Published online:
    14 July 2022
    Print publication:
    04 August 2022
  • A Primer to Theoretical Soil Mechanics is about adapting continuum mechanics to granular materials. The field of continuum mechanics offers many fruitful concepts and methods, however there is declining interest in the field due to its complex and fragmented nature. This book's purpose is therefore to facilitate the understanding of the theoretical principles of soil mechanics, as well as introducing the new theory of barodesy. This title argues for barodesy as a simple alternative to the plasticity theory used currently and provides a systematic insight into this new constitutive model for granular materials. This book therefore introduces a complex field from a fresh and innovative perspective using simple concepts, succinct equations and explanatory sketches. Intended for advanced undergraduates, graduates and PhD students, this title is also apt for researchers seeking advanced training on fundamental topics.

  • 9 - FEA for Linear Time-Dependent Analysis

  • Gang Li, Clemson University, South Carolina
  • Book:
    Introduction to the Finite Element Method and Implementation with MATLAB®
    Published online:
    09 December 2020
    Print publication:
    30 July 2020, pp 463-505

  • Summary

    In this chapter, we discuss the finite element analysis procedure for two types of time-dependent problems: transient heat transfer and structural dynamics (or elastodynamics) problems. In the transient finite element analysis, similar to the discretization of the spatial domain, the continuous time axis is discretized into time steps for time-dependent solutions. Time integration schemes are used to calculate the solution at a given time step by using information already known from previous time steps. The time integration represents the major difference in the solution steps of FEA for time-dependent problems. This chapter contains two sections. The first section introduces the FEA procedure for transient heat transfer analysis by using a 2-D example problem. The second section discusses elastodynamic analysis by demonstrating the procedure of calculating the dynamic response of a 2-D cantilever beam, as well as finding its natural frequencies and vibrational modes. MATLAB codes for solving these problems are presented.