Explicit finite element implementation of a shape memory alloy constitutive model and associated analyses

Shape memory alloys (SMA) represent an important class of smart metallic materials employed in various innovative applications thanks to their unique thermomechanical behavior. Since the 1980s, several SMA constitutive models have been proposed and implemented into both commercial and academic finite element analysis software tools. Such models have demonstrated their reliability and robustness in the design and optimization of a wide variety of SMA-based components. However, most models are implemented using implicit integration schemes, thus limiting their applicability in highly nonlinear analyses. The objective of this work is to present a novel explicit integration scheme for the numerical implementation of the three-dimensional Souza-Auricchio model, a phenomenological model able to reproduce the primary SMA responses (i.e., pseudoelasticity and shape memory effect). The model constitutive equations are formulated by adopting the continuum thermodynamic theory with internal variables, following a plasticity-like approach. An elastic predictor-inelastic corrector scheme is here used to solve the time-discrete non-linear constitutive equations in the explicit framework. The proposed algorithm is investigated through several benchmark boundary-value problems of increasing complexity, considering both pseudoelastic and shape memory response in quasi-static conditions; a comparison with an implicit integration scheme is also performed. Such numerical tests demonstrate the ability of the algorithm to reproduce key material behaviors with effectiveness and robustness. Particularly, the analysis of SMA cables demonstrates the effectiveness of the explicit algorithm to solve complex problems involving widespread nonlinear contact, which prevent the convergence of the implicit scheme. Details such as mass-scaling options are also discussed

Application of a Knowledge-Based Optimization Method for Aerodynamic Design

The current research is investigating the application of an optimization technique to an existing knowledge-based design tool. The optimization method, referred to as CODISC, helps improve the results from a knowledge-based design by eliminating the required advanced design knowledge, or help fine-tune a well-performing vehicle. Three CODISC designs are presented using a generic transonic transport, the Common Research Model (CRM). One design optimizes the baseline CRM to demonstrate the ability to improve a well-performing vehicle. Another design is performed from the CRM with camber and twist removed, which highlights the ability to use CODISC in the conceptual design phase. The final design implements laminar flow on the CRM, showing how CODISC can optimize the extent of laminar flow to find the best aerodynamic performance. All three CODISC designs reduced the vehicle drag compared to the baseline CRM, and highlight the new optimization techniques versatility in the aircraft design industry

Development of a Knowledge-Based Optimization Method for Aerodynamic Design

A new aerodynamic design method, CODISC, has been developed that combines an existing knowledgebased design method, CDISC, with a simple optimization module known as SOUP. The primary goal of this new design system is to improve the performance gains obtained using CDISC without adding significant computational time. An additional benefit of this approach is a reduction in the need for a priori knowledge of good initial input variable values as well as for subsequent manual revisions of those values as the design progresses. A series of 2D and 3D test cases are used to illustrate the development of the process and some of the options available at transonic and supersonic speeds for both laminar and turbulent flow. The test cases start from good baseline configurations and, in all cases, were able to improve the performance. Several new guidelines for good initial values for the design variables, as well new design rules within CDISC itself, were developed from these cases

A Knowledge-Based Optimization Method for Aerodynamic Design

A new aerodynamic design method, CODISC, has been developed that combines a legacy knowledge-based design method, CDISC, with a simple optimization module known as SOUP. The primary goal of this new design system is to improve the performance gains obtained using CDISC without adding significant computational time. An additional objective of this approach is to reduce the need for a priori knowledge of good initial input variable values, as well as for subsequent manual revisions of those values as the design progresses. Several test cases illustrate the development of the process to date and some of the options available at transonic and supersonic speeds for turbulent flow designs. The test cases generally start from good baseline configurations and, in all cases, were able to improve the performance. Several new guidelines for good initial values for the design variables, as well as new design rules within CDISC itself, were developed from these cases

Improving Sparse Representation-Based Classification Using Local Principal Component Analysis

Sparse representation-based classification (SRC), proposed by Wright et al., seeks the sparsest decomposition of a test sample over the dictionary of training samples, with classification to the most-contributing class. Because it assumes test samples can be written as linear combinations of their same-class training samples, the success of SRC depends on the size and representativeness of the training set. Our proposed classification algorithm enlarges the training set by using local principal component analysis to approximate the basis vectors of the tangent hyperplane of the class manifold at each training sample. The dictionary in SRC is replaced by a local dictionary that adapts to the test sample and includes training samples and their corresponding tangent basis vectors. We use a synthetic data set and three face databases to demonstrate that this method can achieve higher classification accuracy than SRC in cases of sparse sampling, nonlinear class manifolds, and stringent dimension reduction.Comment: Published in "Computational Intelligence for Pattern Recognition," editors Shyi-Ming Chen and Witold Pedrycz. The original publication is available at http://www.springerlink.co

Information Splitting for Big Data Analytics

Many statistical models require an estimation of unknown (co)-variance parameter(s) in a model. The estimation usually obtained by maximizing a log-likelihood which involves log determinant terms. In principle, one requires the \emph{observed information}--the negative Hessian matrix or the second derivative of the log-likelihood---to obtain an accurate maximum likelihood estimator according to the Newton method. When one uses the \emph{Fisher information}, the expect value of the observed information, a simpler algorithm than the Newton method is obtained as the Fisher scoring algorithm. With the advance in high-throughput technologies in the biological sciences, recommendation systems and social networks, the sizes of data sets---and the corresponding statistical models---have suddenly increased by several orders of magnitude. Neither the observed information nor the Fisher information is easy to obtained for these big data sets. This paper introduces an information splitting technique to simplify the computation. After splitting the mean of the observed information and the Fisher information, an simpler approximate Hessian matrix for the log-likelihood can be obtained. This approximated Hessian matrix can significantly reduce computations, and makes the linear mixed model applicable for big data sets. Such a spitting and simpler formulas heavily depends on matrix algebra transforms, and applicable to large scale breeding model, genetics wide association analysis.Comment: arXiv admin note: text overlap with arXiv:1605.0764