Stochastic behavior of Mindlin plate with uncertain geometric and material parameters

Monte Carlo simulation-compatible stochastic field for application to expansion-based stochastic finite element method

“…In deriving formulae for the weighted integral method, the element stiffness and the global stiffness as well are demonstrated to be functions of a random variable [3][4][5][6]16], which is defined as a weighted integral (or stochastic integral) as…”

“…Following several decades of extensive analytical and numerical investigations of stochastic systems, several methods are currently available for resolving various engineering problems that involve uncertain system properties, such as random material [1][2][3][4] and/or geometrical parameters [5][6][7] and random excitations [8,9]. The Monte Carlo simulation (MCS), while requiring an effective and accurate tool for numerical generation of random fields, stands at the center of stochastic mechanics, providing a universal means of solving various complicated stochastic problems [10].…”

“…The Monte Carlo simulation (MCS), while requiring an effective and accurate tool for numerical generation of random fields, stands at the center of stochastic mechanics, providing a universal means of solving various complicated stochastic problems [10]. Meanwhile, schemes based on an approximation such as perturbation [11] and expansion-based numerical procedures, known widely as second-moment methods [3][4][5][6][12][13][14], provide alternative methods of solving problems in stochastic mechanics. From the perspective of methodology, the MCS and the Neumann expansion MCS [15] can be categorized as statistical methodologies and the other approximate schemes can be categorized as non-statistical approaches.…”

“…Non-statistical methods, meanwhile, do not directly use random sample fields, but take them into account in an indirect manner. Specifically, they deal with auto-correlation functions [2][3][4][5][6] functions [1] that represent the stochastic field indirectly in terms of correlation distance or wave length, respectively. In the area of non-statistical stochastic analysis, the firstorder expansion scheme is typically employed due to the fact that the computational burden is exponentially increased when a second-or higher-order expansion is employed [16].…”

“…The proposed compatible field can be employed in the conventional first-order weighted integral formulation [3][4][5][6]12] with relative ease. The new proposed formulation has two main advantages when compared to the conventional approaches: a noticeable improvement in the outcomes, i.e., the response variability, and relatively low computation cost when compared to conventional statistical stochastic procedures.…”