Buckling of stochastically heterogeneous beams, using a functional perturbation method

Structural failure investigations through probabilistic nonlinear finite element analysis: Methodology and application

Effect of strength-modulus correlation on reliability of randomly heterogeneous beams

Chatter resistance of non-uniform turning bars with attached dynamic absorbers—Analytical approach

A criterion for the convergence of the stochastic Monte Carlo simulations is necessary to ensure the reliability of their results and to guarantee efficiency. Due to the finite scattering rate in Monte Carlo simulations all quantities are in general correlated in time. This makes the estimation of the stochastic error of the sampled statistics difficult. In this work the theoretical basis of a method found in literature is explored which allows to calculate the stochastic error of stationary Ensemble Monte Carlo simulations and which requires only a rough estimate of the magnitude of the largest correlation time of the sampled quantities. The feasibility of the method is demonstrated by application to substrate current calculations for nMOSFETs.

Light-tissue interactions are commonly studied for near infra-red (NIR) spectroscopy for imaging and diagnosis. While imaging is bound to the surface due to the high tissue scattering, many diagnosis methods, such as the photoplethysmograph (PPG) and pulse oximeter, focus on sensing instead of imaging. There are two approaches for the investigation of light-tissue interactions: one numerical and the other analytical. The most common numerical method is the Monte Carlo (MC) simulation, which is a statistical study of photon migration from the optical properties of the different tissue regions. However, the yield of such statistical approaches is limited. Analytical methods are commonly based on the diffusion theory, yet they are inaccurate near the light source. There are several solution methods, where extrapolated boundary conditions lead to a more accurate solution. Previously, we proposed measuring the full scattering profile (FSP), which is the angular intensity distribution, of cylindrical tissues. MC simulations revealed that the FSP has a fixed intensity point, named the iso-pathlength (IPL) point, which does not depend on the reduced scattering coefficient. The location of this point depends solely on the geometry. In this study, we derived the FSP from the steady state diffusion theory based on the extrapolated zeroboundary condition. A comparison of different reduced scattering coefficients revealed the IPL point, where the intensity remains constant. Furthermore, a MC simulation was performed under the same geometry and optical properties. We show that the position of the IPL according to the diffusion theory is in agreement with the MC simulation.

Because numerical simulation parameters may significantly influence the accuracy of the results, evaluating the sensitivity of simulation results to variations in parameters is essential. Although the field of sensitivity analysis is well developed, systematic application of such methods to complex biological models is limited due to the associated high computational costs and the substantial technical challenges for implementation. In the specific case of the forward problem in electrocardiography, the lack of robust, feasible, and comprehensive sensitivity analysis has left many aspects of the problem unresolved and subject to empirical and intuitive evaluation rather than sound, quantitative investigation. In this study, we have developed a systematic, stochastic approach to the analysis of sensitivity of the forward problem of electrocardiography to the parameter of inhomogeneous tissue conductivity. We apply this approach to a two-dimensional, inhomogeneous, geometric model of a slice through the human thorax. We assigned probability density functions for various organ conductivities and applied stochastic finite elements based on the generalized polynomial chaos-stochastic Galerkin (gPC-SG) method to obtain the standard deviation of the resulting stochastic torso potentials. This method utilizes a spectral representation of the stochastic process to obtain numerically accurate stochastic solutions in a fraction of the time required when employing classic Monte Carlo methods. We have shown that a systematic study of sensitivity is not only easily feasible with the gPC-SG approach but can also provide valuable insight into characteristics of the specific simulation.

This thesis presents a methodology for developing windborne debris (WBD) impact fragility curves for building envelope components (BECs) by using stochastic finite element (FE) models. These fragility curves provide the probabilistic description of the impact resistance of BECs subject to an impact event described by an appropriate intensity measure (IM). Accurate fragility curves are essential in the development of a general probabilistic performance-based engineering framework for mitigation of WBD impact hazard. Monte Carlo simulation is used in combination with the FE method to propagate uncertainties in the BEC’s model parameters and WBD impact location. As an application example, the fragility curves relative to different damage measures are derived for aluminum storm shutters subjected to WBD impact. It is found that (1) the missile kinetic energy at impact is a sufficient IM for BECs with ductile behavior subjected to WBD impact, and (2) the performance of storm panels in terms of penetration of WBDs is critically dependent on the details of the panels’ installation.

Stochastic finite element analysis of composite structures based on material microstructure

Background Accurate biomechanical investigation of human intervertebral discs (IVDs) is difficult because of their complicated structural and material features. Aim To investigate probabilistic distributions of the biomechanical responses of the IVD by considering varying nonlinear structural and material properties using a stochastic finite element (FE) model. Methods A FE model of a L3-4 disc was reconstructed, including the nucleus pulposus (NP), annular matrix and fibers. A Monte Carlo method was used to randomly generate 500 sets of the nonlinear material properties and fiber orientations of the disc that were implemented into the FE model. The FE model was analyzed under seven loading conditions: a 500 N compressive force, a 7.5Nm moment simulating flexion, extension, left-right lateral bending, and left-right axial rotation, respectively. The distributions of the ranges of motion (ROMs), intradiscal pressures (IDP), fiber stresses and matrix strains of the disc were analyzed. Results Under the compressive load, the displacement varied between 0.29 mm and 0.76 mm. Under the 7.5Nm moment, the ROMs varied between 3.0° and 6.0° in primary rotations. The IDPs varied within 0.3 MPa under all the loading conditions. The maximal fiber stress (3.22 ± 0.64 MPa) and matrix strain (0.27 ± 0.12%) were observed under the flexion and extension moments, respectively. Conclusion The IVD biomechanics could be dramatically affected by the structural and material parameters used to construct the FE model. The stochastic FE model that includes the probabilistic distributions of the structural and material parameters provides a useful approach to analyze the statistical ranges of the biomechanical responses of the IVDs.

Reduction of the stochastic finite element models using a robust dynamic condensation method

A stochastic numerical model for wave-induced dynamic response in a spatially heterogeneous seabed around structures

Flooding is and has historically been the most frequent natural disaster in the globe. There is strong evidence that the frequency of flooding is increasing. Pavements, however, are currently designed based on historic climatic conditions assuming a stationary climate, which no longer seems to be a good proxy for future conditions. The goal of this study is to characterize the performance of flooded pavement and quantify the impact of flooding on pavement deterioration and service life. To achieve this goal, the study analyzes the floods occurring in Colorado, United States, in 2013, and uses empirical data on pavement conditions to (1) quantify whether flooding impacts pavement deterioration, (2) define a conceptual model to characterize the deterioration of flooded pavements, and (3) quantify the loss of service life derived from flooding. To address these inquiries, the study used statistical analysis, stochastic Markov deterioration modeling, and Monte Carlo simulations. The study found that flooding accelerates pavement deterioration. Specifically, flooding induces a sudden drop in condition, followed by an accelerated long-term (i.e., multiyear) deterioration that reduces the pavement service life. The better the condition before flooding, the higher the loss of pavement service life. This new understanding of the impact of flooding on pavement conditions will help transportation agencies in the design of resilience programs and postflood strategies. Further research is recommended to analyze other flood events using similar methodologies to understand the influence of factors such as flood characteristics, location, and climate conditions in this phenomenon.

To analyze structural reliability by the stochastic FE (finite element) method rapidly and efficiently, a method combined with the FE method and gradient optimum algorithm based on ANSYS was presented when referring to the geometric interpretation of structural reliability index. ANSYS-based development was adopted to implement it. Results of an example demonstrate that the method requires fewer FE calculations compared with the design point method and Monte-Carlo simulation, and achieves satisfactory accuracy.

The stochastic finite element analysis of elliptic type partial differential equations is considered. A reduced method of the spectral stochastic finite element method using polynomial chaos is proposed. The method is based on the spectral decomposition of the deterministic system matrix. The reduction is achieved by retaining only the dominant eigenvalues and eigenvectors. The response of the reduced system is expanded as a series of Hermite polynomials, and a Galerkin error minimization approach is applied to obtain the deterministic coefficients of the expansion. The moments and probability density function of the solution are obtained by a process similar to the classical spectral stochastic finite element method. The method is illustrated using three carefully selected numerical examples, namely, bending of a stochastic beam, flow through porous media with stochastic permeability and transverse bending of a plate with stochastic properties. The results obtained from the proposed method are compared with classical polynomial chaos and direct Monte Carlo simulation results.

The stochastic-convective model of solute transport was analyzed using interval arithmetic. An interval distribution function was developed to facilitate the identification of appropriate intervals to be used in the proposed interval computing method. Results obtained from a field-scale tracer experiment were used for a relative comparison of three methods (interval computing method, Monte Carlo simulations, and stochastic theories) for predicting travel time distributions and field-scale mean solute concentrations. Interval computations yielded results that agreed well with stochastic approaches and predicted general trends of the observed data. The field-scale solute breakthrough curves were well reproduced by the interval computing method; however, the standard deviations of the travel times were slightly overestimated. The interval computing technique was shown to be computationally efficient and may be viewed as an alternative to the use of stochastic differential equations and Monte Carlo simulation...