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<p>The present study is concerned with a numerical investigation of the stochastic and stationary behavior of fiber-reinforced composite plates with uncertainty about the mechanical and material properties, fiber orientation, and external force. The uncertainty quantification is applied using the Neumann–Monte Carlo Simulation (NMC) and spectral stochastic finite element method (SSFEM) to obtain the estimates of the statistical moments of the solution for composite plate bending problems. The Neumann series acts to obtain the approximation of the inverse of the stochastic stiffness matrix. Fibers derived from the blade of buriti leaves are used to develop volumetric and laminar composites. A composite formed by epoxy mold is used, leading to local variations in mechanical properties such as structural stiffness matrix in structural responses. The finite element formulation (FEM) utilizes spectral stochastic discretization, and a truncated polynomial expansion approximates the random coefficients of the equation system. In the abstract variational problem (AVP), the generalized Hermite functions with unknown coefficients matrix represent the structural variability. The numerical case illustrates the methods’ features, where the uncertainty’s impact is in fiber orientation, volumetric fraction, and vertical displacement. The uncertainty quantification methods are discussed considering that the set of random variables composes a Uniform, Normal, and Gamma distribution. After verifying the convergence of the numerical solution, the first- and second-order statistical moments of the vertical and angular displacement estimators are discussed for the system subjected to the two uncertainty quantification methods. </p>

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Stochastic stationary bending problems of composite plates with different probability distributions

  • 期刊论文

  • 发表日期：

    2025年7月25日

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  • Roberto M. F. Squarcio,
  • João M. Silva Neto,
  • Claudio Roberto Ávila da Silva Junior

摘要

The present study is concerned with a numerical investigation of the stochastic and stationary behavior of fiber-reinforced composite plates with uncertainty about the mechanical and material properties, fiber orientation, and external force. The uncertainty quantification is applied using the Neumann–Monte Carlo Simulation (NMC) and spectral stochastic finite element method (SSFEM) to obtain the estimates of the statistical moments of the solution for composite plate bending problems. The Neumann series acts to obtain the approximation of the inverse of the stochastic stiffness matrix. Fibers derived from the blade of buriti leaves are used to develop volumetric and laminar composites. A composite formed by epoxy mold is used, leading to local variations in mechanical properties such as structural stiffness matrix in structural responses. The finite element formulation (FEM) utilizes spectral stochastic discretization, and a truncated polynomial expansion approximates the random coefficients of the equation system. In the abstract variational problem (AVP), the generalized Hermite functions with unknown coefficients matrix represent the structural variability. The numerical case illustrates the methods’ features, where the uncertainty’s impact is in fiber orientation, volumetric fraction, and vertical displacement. The uncertainty quantification methods are discussed considering that the set of random variables composes a Uniform, Normal, and Gamma distribution. After verifying the convergence of the numerical solution, the first- and second-order statistical moments of the vertical and angular displacement estimators are discussed for the system subjected to the two uncertainty quantification methods.