Microstructure-based stochastic finite element methods for elastostatics and elastodynamics

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Consideration of global boundary value problems in elastostatics of materials with random elastic microstructures leads to the identification of three length scales: macro (global), meso (finite element size), and micro (microstructural heterogeneity). We first provide a formulation of the RVE and mesoscale moduli from the standpoint of elasticity of random media. This is followed by a discussion of basic random field models. These models provide inputs to two finite element schemes - based, respectively, on minimum potential and complementary energy principles - for bounding the global response. While in the classical case of a homogeneous material, these bounds are convergent with the finite elements becoming infinitesimal, the presence of microstructure prevents such a convergence. In the ensemble sense, we obtain micromechanically based stochastic finite elements of elastostatics. Turning to elastodynamics, we first recognize that the dynamics of any structure involves wave propagation in all the members of the structure, and so, a structural dynamics analysis should be based on elastodynamic equations. This is accomplished by a spectral approach where the response of each structural member is described by a stiffness matrix in the frequency space: a spectral finite element. Its stochastic versions are determined for materials described by random Fourier series.

Original languageEnglish (US)
Title of host publication41st Structures, Structural Dynamics, and Materials Conference and Exhibit
StatePublished - 2000
Externally publishedYes
Event41st Structures, Structural Dynamics, and Materials Conference and Exhibit 2000 - Atlanta, GA, United States
Duration: Apr 3 2000Apr 6 2000

Other

Other41st Structures, Structural Dynamics, and Materials Conference and Exhibit 2000
CountryUnited States
CityAtlanta, GA
Period4/3/004/6/00

Fingerprint

Elasticity
Finite element method
Microstructure
Structural members
Structural dynamics
Fourier series
Stiffness matrix
Dynamic analysis
Wave propagation
Boundary value problems
Macros

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Mechanics of Materials
  • Building and Construction
  • Architecture

Cite this

Starzewski, M. O. (2000). Microstructure-based stochastic finite element methods for elastostatics and elastodynamics. In 41st Structures, Structural Dynamics, and Materials Conference and Exhibit

Microstructure-based stochastic finite element methods for elastostatics and elastodynamics. / Starzewski, Martin Ostoja.

41st Structures, Structural Dynamics, and Materials Conference and Exhibit. 2000.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Starzewski, MO 2000, Microstructure-based stochastic finite element methods for elastostatics and elastodynamics. in 41st Structures, Structural Dynamics, and Materials Conference and Exhibit. 41st Structures, Structural Dynamics, and Materials Conference and Exhibit 2000, Atlanta, GA, United States, 4/3/00.
Starzewski MO. Microstructure-based stochastic finite element methods for elastostatics and elastodynamics. In 41st Structures, Structural Dynamics, and Materials Conference and Exhibit. 2000
Starzewski, Martin Ostoja. / Microstructure-based stochastic finite element methods for elastostatics and elastodynamics. 41st Structures, Structural Dynamics, and Materials Conference and Exhibit. 2000.
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