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This work studies the convexity of a class of positive definite probability measures with density functions ρ = c λ ∑ n = 0 ∞ g (n) C n λ w λ , that are generated through the interval characteristic sequences. We discuss when such measures supported in an interval are convex and demonstrate how convexity is preserved under multiplication by certain multipliers and under the intertwining product. A key message to be delivered from this work is: any integrable function f on the interval with a polynomial expansion that has relatively fast absolute convergence, can be decomposed into a non-unique pair of positive convex interval probabilities (f + , f −) ∈ E λ ′ × E λ ′ up to normalization, in the sense that f = f + − f − , where E λ ′ is a class of convex functions. Consequently not only the study of an interval distribution is reduced to the study of the properties of class E λ ′ , but also the discontinuous probabilistic Galerkin schemes can be simplified. As concrete examples the decomposition of polynomials and truncated normal distribution are computed and graphically illustrated. Such interval measures lead to localized spherical probability measures, and as a convex expression of probability measure is a Jensen type inequality for spherical random variables. Based on the spherical information entropy models, one dependent on the domain partition and the other not, we propose three minimization formulations for the probabilistic finite element method, including one that mixes the least-squares and entropy models. • A novel way to decompose an interval distribution into two convex positive parts. • Explore the convexity of interval probability measures by interval characteristic sequences. • Preserve convexity through multipliers and intertwining product. • Build least-squares and entropy mixed spherical model. [ABSTRACT FROM AUTHOR]

Background: The customized prosthesis is a new method for the reconstruction of large mandibular defects. The ability of dental rehabilitation to improve masticatory functions while maintaining the aesthetics of the main anatomy of the patient’s jaw. But the most important problem with all custom prosthesis is the poor performance of screw fixation strength the connections at the bone-plate interface. Materials and Methods: This study was performed to investigate the effect of the number and layout of screws to improve the strength of the bone–prosthesis interface. Due to the inherent variability of input parameters, Analysis of the biomechanical performance of screw fixation strength, a probabilistic finite element method approach has been used. Random input parameters include mechanical properties of the cortical bone, cancellous bone, titanium alloy (Ti6Al4V), and bite force. The layout of the screws was designed in 6 models. Criteria for evaluating the biomechanical performance of screw fixation strength include maximum stress and strain of von Mises cortical bone around the screws. The Monte-Carlo method was used for finite element simulation. Results: The most critical screw in all models is screw No.1, which by increasing the number of screws and correcting the layout shape, the values of maximum stress and strain in the bone around screw No.1 has decreased by 26.7% and 46.3%, respectively, and increased the reliability of the screw connection performance by 25% and 28%, respectively. Conclusion: Finally, in the reconstruction of a large lateral mandibular defect by the customized prosthesis, the strength of the prosthesis to connect to the remaining mandible bone can be improved by increasing the number and modifying the layout of the screws. Keywords: Mandible reconstruction; Customized prosthesis; Probabilistic finite element method; Reliability.

The present work deals with the development of a finite element methodology for obtaining the stress distributions in thick cylindrical HK40 stainless steel pipe that carries high-temperature fluids. The material properties and loading were assumed to be random variables. Thermal stresses that are generated along radial, axial, and tangential directions are generally computed using very complex analytical expressions. To circumvent such an issue, probability theory and mathematical statistics have been applied to many engineering problems, which allows determination of the safety both quantitatively and objectively based on the concepts of reliability. Monte Carlo simulation methodology is used to study the probabilistic characteristics of thermal stresses, and was implemented to estimate the probabilistic distributions of stresses against the variations arising due to material properties and load. A 2-D probabilistic finite element code was developed in MATLAB, and the deterministic solution was compared with ABAQUS solutions. The values of stresses obtained from the variation of elastic modulus were found to be low compared to the case where the load alone was varying. The probability of failure of the pipe structure was predicted against the variations in internal pressure and thermal gradient. These finite element framework developments are useful for the life estimation of piping structures in high-temperature applications and for the subsequent quantification of the uncertainties in loading and material properties.

Abstract: The integrated design method of series traction rod of heavy machinery was studied. Based on topology optimization, parameter optimization design and reliability analysis, its integrated design method was proposed. Its topology optimization design and parameter optimization design were done. Moreover, based on probabilistic finite element method, the influence of the randomness of the design parameters to its maximum deflection and maximum equivalent stress was studied. The method and basis are supported for design and development of series traction rod of heavy machinery. [Copyright &y& Elsevier]