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Machine Learning (ML) algorithms are increasingly used as surrogate models to increase the efficiency of stochastic reliability analyses in geotechnical engineering. This paper presents a highly efficient ML aided reliability technique that is able to accurately predict the results of a Monte Carlo (MC) reliability study, and yet performs 500 times faster. A complete MC reliability analysis on anisotropic heterogeneous slopes consisting of 120,000 simulated samples is conducted in parallel to the proposed ML aided stochastic technique. Comparing the results of the complete MC study and the proposed ML aided technique, the expected errors of the proposed method are realistically examined. Circumventing the time-consuming computation of factors of safety for the training datasets, the proposed technique is more efficient than previous methods. Different ML models, including Random Forest (RF), Support Vector Machine (SVM) and Artificial Neural Networks (ANN) are presented, optimised and compared. The effects of the size and type of training and testing datasets are discussed. The expected errors of the ML predicted probability of failure are characterised by different levels of soil heterogeneity and anisotropy. Using only 1% of MC samples to train ML surrogate models, the proposed technique can accurately predict the probability of failure with mean errors limited to 0.7%. The proposed technique reduces the computational time required for our study from 306 days to only 14 hours, providing 500 times higher efficiency.

Random field Monte Carlo (MC) reliability analysis is a robust stochastic method to determine the probability of failure. This method, however, requires a large number of numerical simulations demanding high computational costs. This paper explores the efficiency of different machine learning (ML) algorithms used as surrogate models trained on a limited number of random field slope stability simulations in predicting the results of large datasets. The MC data in this paper require only the examination of failure or non-failure, circumventing the time-consuming calculation of factors of safety. An extensive dataset is generated, consisting of 120,000 finite difference MC slope stability simulations incorporating different levels of soil heterogeneity and anisotropy. The Bagging Ensemble, Random Forest and Support Vector classifiers are found to be the superior models for this problem amongst 9 different models and ensemble classifiers. Trained only on 0.47% of data (500 samples), the ML model can classify the entire 120,000 samples with an accuracy of %85 and AUC score of %91. The performance of ML methods in classifying the random field slope stability results generally reduces with higher anisotropy and heterogeneity of soil. The ML assisted MC reliability analysis proves a robust stochastic method where errors in the predicted probability of failure using %5 of MC data is only %0.46 in average. The approach reduced the computational time from 306 days to less than 6 hours.

Many experiments have shown large flow enhancement ratios (up to 10^5) in carbon nanotubes (CNT) with diameters larger than 5nm. However, molecular dynamics simulations have never replicated these results maintaining a three-order-of-magnitude gap with measurements. Our study provides a generic model of nanofluidics for continuum slip flow (diameter>3nm) that fills this significant gap and sheds light on its origin. Compared to 140 literature cases, the model explains the entire range of experimental flow enhancements by changes of nanotube diameters and finite variations of interfacial energies. Despite large variations of flow enhancement ratios spanning 5 orders of magnitude in experimental results, the ratio between these data and corresponding model predictions approaches unity for the majority of experiments. The role of viscous entrance effects is discussed. The model provides insight into puzzling observations such as differences of CNTs and boron nitride nanotubes, the slip on low-contact-angle surfaces and massive functionalization effects. This study could advance our understanding of nano-scale transport mechanisms and aid the design of tailored nanomembranes.

The work reported here pertains only to the first year of research for a three year proposal period. As a prelude to this two dimensional interface element, the one dimensional element was tested and errors were discovered in the code for built-up structures and curved interfaces. These errors were corrected and the benchmark Boeing composite crown panel was analyzed successfully. A study of various splines led to the conclusion that cubic B-splines best suit this interface element application. A least squares approach combined with cubic B-splines was constructed to make a smooth function from the noisy data obtained with random error in the coordinate data points of the Boeing crown panel analysis. Preliminary investigations for the formulation of discontinuous 2-D shell and 3-D solid elements were conducted.

The implementation of an interface element capability within the COMET-AR software system is described. The report is intended for use by both users of currently implemented interface elements and developers of new interface element formulations. Guidance on the use of COMET-AR is given. A glossary is provided as an Appendix to this report for readers unfamiliar with the jargon of COMET-AR. A summary of the currently implemented interface element formulation is presented in Section 7.3 of this report.

A method for analyzing global/local behavior of plate and shell structures is described. In this approach, a detailed finite element model of the local region is incorporated within a coarser global finite element model. The local model need not be nodally compatible (i.e., need not have a one-to-one nodal correspondence) with the global model at their common boundary; therefore, the two models may be constructed independently. The nodal incompatibility of the models is accounted for by introducing appropriate constraint conditions into the potential energy in a hybrid variational formulation. The primary advantage of this method is that the need for transition modeling between global and local models is eliminated. Eliminating transition modeling has two benefits. First, modeling efforts are reduced since tedious and complex transitioning need not be performed. Second, errors due to the mesh distortion, often unavoidable in mesh transitioning, are minimized by avoiding distorted elements beyond what is needed to represent the geometry of the component. The method is applied reduced to a plate loaded in tension and transverse bending. The plate has a central hole, and various hole sixes and shapes are studied. The method is also applied to a composite laminated fuselage panel with a crack emanating from a window in the panel. While this method is applied herein to global/local problems, it is also applicable to the coupled analysis of independently modeled components as well as adaptive refinement.

A new interface element based on the hybrid variational formulation is presented and demonstrated. The element provides a means of connecting independently modeled substructures whose nodes along the common boundary need not be coincident. The interface element extends previous work to include connecting an arbitrary number of substructures, the use of closed and generally curved interfaces, and the use of multiple, possibly nested, interfaces. Several applications of the element are presented and aspects of the implementation are discussed.

Hybrid shell elements have long been regarded with reserve by the commercial finite element developers despite the high degree of reliability and accuracy associated with such formulations. The fundamental reason is the inherent higher computational cost of the hybrid approach as compared to the displacement-based formulations. However, a noteworthy factor in favor of hybrid elements is that numerical integration to generate element matrices can be entirely avoided by the use of symbolic integration. In this paper, the use of the symbolic computational approach is presented for an assumed-stress hybrid shell element with drilling degrees of freedom and the significant time savings achieved is demonstrated through an example.

Computational methods for global/local analysis of structures which include both uncoupled and coupled methods are described. In addition, global/local analysis methodology for automatic refinement of incompatible global and local finite element models is developed. Representative structural analysis problems are presented to demonstrate the global/local analysis methods.

An improved four-node quadrilateral assumed-stress hybrid shell element with drilling degrees of freedom is presented. The formulation is based on Hellinger-Reissner variational principle and the shape functions are formulated directly for the four-node element. The element has 12 membrane degrees of freedom and 12 bending degrees of freedom. It has nine independent stress parameters to describe the membrane stress resultant field and 13 independent stress parameters to describe the moment and transverse shear stress resultant field. The formulation encompasses linear stress, linear buckling, and linear free vibration problems. The element is validated with standard tests cases and is shown to be robust. Numerical results are presented for linear stress, buckling, and free vibration analyses.

A simple 4-node assumed-stress hybrid quadrilateral shell element with rotational or 'drilling' degrees of freedom is formulated. The element formulation is based directly on a 4-node element rather than being derived from an 'internal' 8-node isoparametric element. The formulation is based on the principle of minimum complementary energy. The membrane part of the element has 12 degrees of freedom. The bending part of the element also has 12 degrees of freedom. The bending part of the element uses the Reissner-Mindlin plate theory which takes into account the transverse shear effects. Quadratic variations for both in-plane and out-of-plane displacement fields and linear variations for both in-plane and out-of-plane rotation fields are assumed along the edges of the element. The element passes the patch test, is nearly insensitive to mesh distortion, has no spurious modes, and is invariant with respect to node numbering.

An assumed-stress hybrid/mixed 4-node quadrilateral shell element is introduced that alleviates most of the deficiencies associated with such elements. The formulation of the element is based on the assumed-stress hybrid/mixed method using the Hellinger-Reissner variational principle. The membrane part of the element has 12 degrees of freedom including rotational or drilling degrees of freedom at the nodes. The bending part of the element also has 12 degrees of freedom. The bending part of the element uses the Reissner-Mindlin plate theory which takes into account the transverse shear contributions. The element formulation is derived from an 8-node isoparametric element. This process is accomplished by assuming quadratic variations for both in-plane and out-of-plane displacement fields and linear variations for both in-plane and out-of-plane rotation fields along the edges of the element. In addition, the degrees of freedom at midside nodes are approximated in terms of the degrees of freedom at corner nodes. During this process the rotational degrees of freedom at the corner nodes enter into the formulation of the element. The stress field are expressed in the element natural-coordinate system such that the element remains invariant with respect to node numbering.

The Computational Structural Mechanics (CSM) activity is developing advanced structural analysis and computational methods that exploit high-performance computers. Methods are developed in the framework of the CSM testbed software system and applied to representative complex structural analysis problems from the aerospace industry. An overview of the CSM testbed methods development environment is presented and some numerical methods developed on a CRAY-2 are described. Selected application studies performed on the NAS CRAY-2 are also summarized.

The initial Computational Structural Mechanics (CSM) Testbed was based on Level 13 of the SPAR finite element computer program. Until recently, the element library of the Testbed has been limited to those elements in Level 13 of SPAR. The development of a generic element processor has enabled element researchers to develop, implement and assess element formulations with relative ease. An assessment of new elements as well as the existing SPAR Level 13 elements has revealed some definite shortcomings with the SPAR Level 13 2-D and 3-D elements. The SPAR S81 solid element does not pass the patch test problem proposed by MacNeal-Harder. These deficiencies are identified here. The 2-D elements, however, seem to perform well taking into account the limitations imposed by the theory used to formulate them, (i.e., thin plates only). Common deficiencies of the 2-D and 3-D elements in SPAR have to do with their adaptability to the nonlinear analysis utilities developed by Lockheed Palo Alto Research Lab. Also, the EFIL format of the SPAR element data does not conform to the standard format of the Testbed.