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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]

The aim of this study was to design for mandibular reconstruction of large lateral defect with minimum target reliability with designated confidence interval under bite force range of 300 ± 102 N. The performance of the models has been evaluated by numerical analysis considering the uncertainty of input parameters. Computer-Aided design was used to develop the models of three designs according to the patient's anatomy and to achieve to near symmetry of the mandible. Stress-strength modeling was utilized for the probabilistic physics of failure analysis under assumption of a quasi-static load. Monte-Carlo simulation was also applied for probabilistic finite element analysis and reliability assessment. The sensitivity analysis of the models was developed to reflect the significance of the variables in the models. The deterministic stress analysis shows that the highest stress and the second maximum stress are 110 MPa and 85 MPa for cortical bone around the screws, respectively. Also, it is determined that the maximum plate stress of the titanium conventional plate model is 580 MPa. The reconstruction system success rate was improved in all models by observing the anatomy of the patient's mandible in the plate designs by computer-aided design and additive manufacturing techniques. Based on the results, the reliability of plate strength and pull-out screws strength are 99.99% and 96.71% for the fibula free flap model, respectively, and 99.99% and 94.17%, respectively, for the customized prosthesis model. Probability sensitivity factors showed that uncertainty in the elastic modulus of the cortical bone has the greatest effect on the probability of screws loosening. [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.

This paper deals with the slope stability problem by a finite element reliability analysis considering the spatial variation of soil strength parameters. In this work, the spatial variation is described using random field theory. To simplify the implementation of the proposed procedure for slope reliability analysis, elastic perfectly plastic constitutive model describing the soil behaviour using the Mohr coulomb yield criterion is adopted. The application of the proposed approach for the slope reliability analysis is performed using a performance function expressed in terms of stress fields mobilised along a circular failure surface. For this purpose, a computation of the stress gradient based on the incremental theory of plasticity is used. The results of the proposed procedure are checked by a probabilistic method based on the combination of the Bishop's model and the Monte Carlo simulation. The numerical examples have elucidated the efficiency and the validity of the present procedure to slope reliability analysis. Finally, the proposed procedure is applied for locating critical probabilistic circular sliding surface considering the spatial variation of the shear strength parameters. [ABSTRACT FROM PUBLISHER]

The present study investigates the influence of material uncertainty on the dynamic response of functionally graded graphene nanoplatelets (FG-GPLs) reinforced porous spherical panels under air blast loading. The uncertainty is included in various parameters such as Young's moduli, mass density, Poisson's ratios, porosity coefficient, and GPLs' weight fraction. The microstructural gradation is accomplished by creating pores followed by symmetric, asymmetric, and uniform porosity distributions which lead to variation in the properties along the thickness direction. The metal matrix i.e., Aluminum is reinforced with graphene nano-platelets, and the effective Young's modulus is estimated using the Halpin–Tsai model whereas the rule of the mixture is employed to determine effective mass density and Poisson's ratio. A higher-order C 0 — continuous structural kinematics is employed to find the dynamic response of the spherical panels. The Governing relations are developed using Euler–Lagrange's equation and the finite element method in conjunction with the first-order perturbation technique and Newmark's time integration scheme is applied to find the numerical results in terms of mean and standard deviation of center displacement. The influence of various parameter such as porosity coefficient, GPLs weight fraction, TNT-weight, stand-off stand, etc. are also presented in detail. • The influence of material uncertainty on FG-GPLs reinforced porous spherical panels subjected to air blast loading is studied for the first time. • The dynamic response of blast-loaded panels is investigated in deterministic and probabilistic frameworks. • The mean and standard deviation of the dynamic response associated with the panels have been examined. • A probabilistic finite element approach based on the first-order perturbation technique is adopted as a solution methodology. [ABSTRACT FROM AUTHOR]

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]