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• A hybrid reliability-based heat dissipation structural design optimization model is established for the practical heat dissipation problem with the interval distribution parameters. • Two equivalent triple-loop hybrid reliability-based heat dissipation structural design optimization models are established. • An efficient single-loop method is proposed to solve hybrid reliability-based heat dissipation structural design optimization the model. The conventional reliability-based heat dissipation structural design optimization, which fully considers the influence of the random uncertainties in the optimization procedure, can provide an optimum design satisfying the reliability requirements of the heat radiating device. However, in practical heat dissipation design problems, especially in the early stage of structural design which lacks the corresponding experimental data, some crucial distribution parameters of the random uncertainties, may not be determined precisely. This paper establishes a hybrid reliability-based heat dissipation structural design optimization model for the problem with limited information based on a kind of probability-interval hybrid quantification model and proposes a single-loop method to solve this model efficiently. In this optimization model, the interval parameters coupled to the random uncertainties lead to an interval of reliability for each constraint function, thus giving rise to a triple-loop optimization problem. The proposed single-loop method firstly converts the original nested triple-loop optimization model into an equivalent double-loop optimization model through monotonic analysis. Then, the Karush-Kuhn-Tucker (KKT) optimality conditions of the inner loop are enforced to convert the double-loop model into an equivalent single-loop optimization model. Through this treatment, the original triple-loop optimization model can be then solved by a series of design deterministic optimization and the computational demand can be alleviated significantly. The efficiency and accuracy of the proposed single-loop method are verified through several numerical problems. [ABSTRACT FROM AUTHOR]

Recently, a mixed finite element-least square point interpolation method (FE-LSPIM) has been extended to deal with 2D acoustic problem by the authors. That element employed radial-polynomial basis functions for the local approximation (LA). This paper presents a FE-Meshfree QUAD4 element for analyzing the two dimensions (2D) and three dimensions (3D) acoustic problem by combining the excellent property of FE and radial-polynomial basis point interpolation shape functions by utilizing the partition of unity (PU) principles methods. In this work, the acoustic domain is discretized by quadrilateral mesh, and then the shape functions of quadrilateral element and the radial point interpolation are used for the LA. The radial-polynomial basis capacitates the proposed method to free from the possible singularity of the moment matrix that could sometimes result with an inappropriate choice of polynomial basis functions. The present method also offers an “appropriate-stiff” model for reducing the numerical dispersion error as compared to the previous FEM or FE-LSPIM with pure polynomial basis, especially for the high wave number problem. These findings have been validated through several numerical test problems. [ABSTRACT FROM AUTHOR]

• An efficient framework for structural time-variant reliability analysis is proposed. • The adaptive accuracy of outcrossing rate is provided by the FOTRE method. • The explicit formulation of reliability index and sensitivity direction is given. Time-variant reliability problems are frequently encountered in engineering due to factors like material degradation or random loading modeled as random processes. The PHI2 method, which employs the First Order Reliability Method (FORM), is commonly used to solve such problems. However, it requires repeated searches for Most Probable Points (MPPs), making it computationally expensive. To improve efficiency with little sacrifice of accuracy, this study proposes a First Order Time-variant Reliability Expansion (FOTRE) method, which provides an efficient explicit formulation for MPP regarding time, in contrast to the expensive optimization approach of the PHI2 method. It requires only a single accurate search for the so-called "worst MPP" over the whole lifespan and offers the " adaptive accuracy of outcrossing rate ", which avoids the repeated search for MPPs ensuring computational accuracy. The inspiration behind the FOTRE method stems from the observation that the outcrossing rate tends to be small at time points with relatively large reliability indexes compared to the minimum reliability index β min , which has a negligible impact on the subsequent structural failure probability over the entire lifespan. This innovative approach significantly improves the efficiency of solving time-variant reliability problems without compromising much of the numerical accuracy. The effectiveness and accuracy of the FOTRE method are demonstrated through several numerical examples. [ABSTRACT FROM AUTHOR]

• A transient temperature response analysis method based on the interval K-L expansion is proposed. • The time-variant uncertain parameters are quantified by an interval process model due to lack of sufficient sample data. • The analytical solution for the upper and lower bounds of the transient temperature responses are given. A transient temperature response analysis method for heat transfer problems with dynamic uncertain parameters is proposed. The time-variant or dynamic uncertain parameters are quantified by an interval process model using only the variation bounds of uncertainty, providing an effective way for problems where probabilistic modeling of the dynamic uncertainties is unfeasible due to lack of sufficient sample data. The interval Karhunen–Loève (K-L) expansion is adopted to represent the interval processes, thus describing accurately the continuous uncertainty over time by a series of interval variables. For convenience of solution, the Laplace transformation is then applied to transform the heat transfer uncertainty analysis over time domain to the complex field, where the analytical solution for the upper and lower bounds of the transient temperature responses can be obtained. Finally, the computational effectiveness and efficiency of the proposed method are verified by three typical numerical examples. [ABSTRACT FROM AUTHOR]