High Order IMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings

In this paper,we consider the high order method for solving the linear transport equations under diffusive scaling and with random inputs.To tackle the randomness in the problem,the stochastic Galerkin method of the generalized polynomial chaos approach has been employed.Besides,the high order implicit-explicit scheme under the micro-macro decomposition framework and the discontinuous Galerkin method have been employed.We provide several numerical experiments to validate the accuracy and the stochastic asymptotic-preserving property.

Probabilistic stability of uncertain composite plates and stochastic irregularity in their buckling mode shapes:A semi-analytical non-intrusive approach

In this study,the mechanical properties of the composite plate were considered Gaussian random fields and their effects on the buckling load and corresponding mode shapes were studied by developing a semi-analytical nonintrusive approach.The random fields were decomposed by the Karhunen−Loève method.The strains were defined based on the assumptions of the first-order and higher-order shear-deformation theories.Stochastic equations of motion were extracted using Euler-Lagrange equations.The probabilistic response space was obtained by employing the nonintrusive polynomial chaos method.Finally,the effect of spatially varying stochastic properties on the critical load of the plate and the irregularity of buckling mode shapes and their sequences were studied for the first time.Our findings showed that different shear deformation plate theories could significantly influence the reliability of thicker plates under compressive loading.It is suggested that a linear relationship exists between the mechanical properties’variation coefficient and critical loads’variation coefficient.Also,in modeling the plate properties as random fields,a significant stochastic irregularity is obtained in buckling mode shapes,which is crucial in practical applications.

Uncertainty propagation in dynamics of composite plates: A semi-analytical non-sampling-based approach

In this study,the influences of spatially varying stochastic properties on free vibration analysis of composite plates were investigated via development of a new approach named the deterministic-stochastic Galerkin-based semi-analytical method.The material properties including tensile modulus,shear modulus,and density of the plate were assumed to be spatially varying and uncertain.Gaussian fields with first-order Markov kernels were utilized to define the aforementioned material properties.The stochastic fields were decomposed via application of the K arhunen-Loeve theorem.A first-order shear deformation theory was assumed,following which the displacement field was defined using admissible trigonometric modes to derive the potential and kinetic energies.The stochastic equations of motion of the plate were obtained using the variational principle.The deterministic-stochastic Galerkin-based method was utilized to find the probability space of natural frequencies,and the corresponding mode shapes of the plate were determined using a polynomial chaos approach.The proposed method significantly reduced the size of the mathematical models of the structure,which is very useful for enhancing the computational efficiency of stochastic simulations.The methodology was verifed using a stochastic finite element method and the available results in literature.The sensitivity of natural frequencies and corresponding mode shapes due to the uncertainty of material properties was investigated,and the results indicated that the higher-order modes are more sensitive to uncertainty propagation in spatially varying properties.

Introducing a New Tool for Studying Unstable Systems

This paper presents the starting project of a web site focussed on unstable systems. It is a web-based database in a bilingual version(English/Czech), which can be used as an information database for models of unstable processes. The web site contains the mathematical models of such systems, including their simulation files together with basic information about the stability of dynamic systems. The paper outlines the motivation for the development of this database, presents its basic structure, and discusses several models from the site. The areas of prospective usage are also suggested together with the possible directions of further development of this project. The contribution ends with a case study using the database for control system analysis and design of the Amira inverted pendulum. The systematic polynomial approach is fruitfully utilised for the task together with some useful tools from the robust control theory.