http://hdl.handle.net/1721.1/35730 http://hdl.handle.net/1721.1/35825 Smoothed Finite Element Method Dai, K.Y. Liu, Guirong In this paper, the smoothed finite element method (SFEM) is proposed for 2D elastic problems by incorporation of the cell-wise strain smoothing operation into the conventional finite elements. When a constant smoothing function is chosen, area integration becomes line integration along cell boundaries and no derivative of shape functions is needed in computing the field gradients. Both static and dynamic numerical examples are analyzed in the paper. Compared with the conventional FEM, the SFEM achieves more accurate results and generally higher convergence rate in energy without increasing computational cost. In addition, as no mapping or coordinate transformation is performed in the SFEM, the element is allowed to be of arbitrary shape. Hence the well-known issue of the shape distortion of isoparametric elements can be resolved. http://hdl.handle.net/1721.1/35824 Reduced Basis Approximation and A Posteriori Error Estimation for Stress Intensity Factors: Application to Failure Analysis Huynh, Dinh Bao Phuong Peraire, Jaime Patera, Anthony T. Liu, Guirong This paper reports the development of reduced basis approximations, rigorous a posteriori error bounds, and offline-online computational procedures for the accurate, fast and reliable predictions of stress intensity factors or strain energy release rate for “Mode I” linear elastic crack problem. We demonstrate the efficiency and rigor of our numerical method in several examples. We apply our method to a practical failure design application. http://hdl.handle.net/1721.1/35823 Linear Thermodynamics of Rodlike DNA Filtration Li, Zirui Liu, Guirong Chen, Yuzong Wang, Jian-Sheng Hadjiconstantinou, Nicolas Cheng, Y. Han, J. Linear thermodynamics transportation theory is employed to study filtration of rodlike DNA molecules. Using the repeated nanoarray consisting of alternate deep and shallow regions, it is demonstrated that the complex partitioning of rodlike DNA molecules of different lengths can be described by traditional transport theory with the configurational entropy properly quantified. Unlike most studies at mesoscopic level, this theory focuses on the macroscopic group behavior of DNA transportation. It is therefore easier to conduct validation analysis through comparison with experimental results. It is also promising in design and optimization of DNA filtration devices through computer simulation. http://hdl.handle.net/1721.1/35822 An Efficient Reduced-Order Approach for Nonaffine and Nonlinear Partial Differential Equations Nguyen, N. C. Peraire, Jaime In the presence of nonaffine and highly nonlinear terms in parametrized partial differential equations, the standard Galerkin reduced-order approach is no longer efficient, because the evaluation of these terms involves high computational complexity. An efficient reduced-order approach is developed to deal with “nonaffineness” and nonlinearity. The efficiency and accuracy of the approach are demonstrated on several test cases, which show significant computational savings relative to classical numerical methods and relative to the standard Galerkin reduced-order approach.