New twelve node serendipity quadrilateral plate bending element based on Mindlin-Reissner theory using Integrated Force Method

The Integrated Force Method (IFM) is a novel matrix formulation developed for analyzing the civil, mechanical and aerospace engineering structures. In this method all independent/internal forces are treated as unknown variables which are calculated by simultaneously imposing equations of equilibrium and compatibility conditions. This paper presents a new 12-node serendipity quadrilateral plate bending element MQP12 for the analysis of thin and thick plate problems using IFM. The Mindlin-Reissner plate theory has been employed in the formulation which accounts the effect of shear deformation. The performance of this new element with respect to accuracy and convergence is studied by analyzing many standard benchmark plate bending problems. The results of the new element MQP12 are compared with those of displacement-based 12-node plate bending elements available in the literature. The results are also compared with exact solutions. The new element MQP12 is free from shear locking and performs excellent for both thin and moderately thick plate bending situations.

Deformational Behavior of Fiber-Reinforced Concrete Beams in Bending

An experimental study aimed at understanding the deformational behavior of conventionally reinforced steel fiber concrete beams in pure bending is reported in this paper. One group of beams has steel fibers dispersed in the entire volume of the beam and the second has fibers dispersed over half the depth of the beam on the tension side. A comparative study of the deformational characteristics of these beams has been made. Half-depth fiber inclusion, requiring only half the quantity of fibers of full-depth inclusion, is found to be equally effective in improving the deformational behavior of beams. Thus, by such modes of inclusion of fibers, an economical and efficient use of expensive steel fibers can be realized.

Kinetic approach to dislocation bending in low-mobility films

A kinetic model has been developed for dislocation bending at the growth surface in compressively stressed low-mobility films such as III-V nitrides. It is based on a reduction in the number of atoms at the growth surface. Stress and nonstress sources of driving force for such a reduction are discussed. A comparison between the derived equations and experimentally measured stress evolution data yields good agreement between the predicted and observed angles through which dislocations bend.

Fracture Analysis of Concrete Structural Components Accounting for Tension Softening Effect

This paper presents methodologies for fracture analysis of concrete structural components with and without considering tension softening effect. Stress intensity factor (SIF) is computed by using analytical approach and finite element analysis. In the analytical approach, SW accounting for tension softening effect has been obtained as the difference of SIP obtained using linear elastic fracture mechanics (LEFM) principles and SIP due to closing pressure. Superposition principle has been used by accounting for non-linearity in incremental form. SW due to crack closing force applied on the effective crack face inside the process zone has been computed using Green's function approach. In finite element analysis, the domain integral method has been used for computation of SIR The domain integral method is used to calculate the strain energy release rate and SIF when a crack grows. Numerical studies have been conducted on notched 3-point bending concrete specimen with and without considering the cohesive stresses. It is observed from the studies that SW obtained from the finite element analysis with and without considering the cohesive stresses is in good agreement with the corresponding analytical value. The effect of cohesive stress on SW decreases with increase of crack length. Further, studies have been conducted on geometrically similar structures and observed that (i) the effect of cohesive stress on SW is significant with increase of load for a particular crack length and (iii) SW values decreases with increase of tensile strength for a particular crack length and load.

Verifying scalings for bending rigidity of bilayer membranes using mesoscale models

The bending rigidity kappa of bilayer membranes was studied with coarse grained soft repulsive potentials using dissipative particle dynamics (DPD) simulations. Using a modified Andersen barostat to maintain the bilayers in a tensionless state, the bending rigidity was obtained from a Fourier analysis of the height fluctuations. From simulations carried out over a wide range of membrane thickness, the continuum scaling relation kappa proportional to d(2) was captured for both the L-alpha and L-beta phases. For membranes with 4 to 6 tail beads, the bending rigidity in the L-beta phase was found to be 10-15 times higher than that observed for the L-alpha phase. From the quadratic scalings obtained, a six fold increase in the area stretch modulus, k(A) was observed across the transition. The magnitude of increase in both kappa and k(A) from the L-alpha to the L-beta phase is consistent with current experimental observations in lipid bilayers and to our knowledge provides for the first time a direct evaluation of the mechanical properties in the L-beta phase.

Lamination-dependent shear deformation models for bending of angle-ply laminated plates

Lamination-dependent shear corrective terms in the analysis of bending of laminated plates are derived from a priori assumed linear thicknesswise distributions for gradients of transverse shear stresses by using CLPT inplane stresses in the two in-plane equilibrium equations of elasticity in each ply. In the development of a general model for angle-ply laminated plates, special cases like cylindrical bending of laminates in either direction, symmetric laminates, cross-ply laminates, antisymmetric angle-ply laminates, homogeneous plates are taken into consideration. Adding these corrective terms to the assumed displacements in (i) Classical Laminate Plate Theory (CLPT) and (ii) Classical Laminate Shear Deformation Theory (CLSDT), two new refined lamination-dependent shear deformation models are developed. Closed form solutions from these models are obtained for antisymmetric angle-ply laminates under sinusoidal load for a type of simply supported boundary conditions. Results obtained from the present models and also from Ren's model (1987) are compared with each other.

Lamination-dependent shear deformation models for cylindrical bending of angle-ply laminates

Lamination-dependent shear corrective terms in the analysis of flexure of laminates are derived from a priori assumed linear thicknesswise distributions for gradients of transverse shear stresses and using them in the two in-plane equilibrium equations of elasticity in each ply. Adding these corrective terms to (i) Classical Laminate Plate Theory (CLPT) displacements and (ii) Classical Laminate Shear Deformation Theory (CLSDT) displacements, four new refined lamination-dependent shear deformation models for angle-ply laminates are developed. Performance of these models is evaluated by comparing the results from these models with those from exact elasticity solutions for antisymmetric 2-ply laminates and for 4-ply [15/-15](s) laminates. In general, the model with shear corrective terms based on CLPT and added to CLSDT displacements is sufficient and predicts good estimates, both qualitatively and quantitatively, for all displacements and stresses.

The complexity of certain incremental code generation problems

This paper looks at the complexity of four different incremental problems. The following are the problems considered: (1) Interval partitioning of a flow graph (2) Breadth first search (BFS) of a directed graph (3) Lexicographic depth first search (DFS) of a directed graph (4) Constructing the postorder listing of the nodes of a binary tree. The last problem arises out of the need for incrementally computing the Sethi-Ullman (SU) ordering [1] of the subtrees of a tree after it has undergone changes of a given type. These problems are among those that claimed our attention in the process of our designing algorithmic techniques for incremental code generation. BFS and DFS have certainly numerous other applications, but as far as our work is concerned, incremental code generation is the common thread linking these problems. The study of the complexity of these problems is done from two different perspectives. In [2] is given the theory of incremental relative lower bounds (IRLB). We use this theory to derive the IRLBs of the first three problems. Then we use the notion of a bounded incremental algorithm [4] to prove the unboundedness of the fourth problem with respect to the locally persistent model of computation. Possibly, the lower bound result for lexicographic DFS is the most interesting. In [5] the author considers lexicographic DFS to be a problem for which the incremental version may require the recomputation of the entire solution from scratch. In that sense, our IRLB result provides further evidence for this possibility with the proviso that the incremental DFS algorithms considered be ones that do not require too much of preprocessing.

Incremental-angle and angular velocity estimation using a star sensor

A method is described for estimating the incremental angle and angular velocity of a spacecraft using integrated rate parameters with the help of a star sensor alone. The chief advantage of this method is that the measured stars need not be identified, whereas the identification of the stars is necessary in earlier methods. This proposed estimation can be carried out with all of the available measurements by a simple linear Kalman filter, albeit with a time-varying sensitivity matrix. The residuals of estimated angular velocity by the proposed spacecraft incremental-angle and angular velocity estimation method are as accurate as the earlier methods. This method also enables the spacecraft attitude to be reconstructed for mapping the stars into an imaginary unit sphere in the body reference frame, which will preserve the true angular separation of the stars. This will pave the way for identification of the stars using any angular separation or triangle matching techniques applied to even a narrow field of view sensor that is made to sweep the sky. A numerical simulation for inertial as well as Earth pointing spacecraft is carried out to establish the results.

Faster Algorithms for Incremental Topological Ordering.Robert Tarjan

We present two online algorithms for maintaining a topological order of a directed acyclic graph as arcs are added, and detecting a cycle when one is created. Our first algorithm takes O(m 1/2) amortized time per arc and our second algorithm takes O(n 2.5/m) amortized time per arc, where n is the number of vertices and m is the total number of arcs. For sparse graphs, our O(m 1/2) bound improves the best previous bound by a factor of logn and is tight to within a constant factor for a natural class of algorithms that includes all the existing ones. Our main insight is that the two-way search method of previous algorithms does not require an ordered search, but can be more general, allowing us to avoid the use of heaps (priority queues). Instead, the deterministic version of our algorithm uses (approximate) median-finding; the randomized version of our algorithm uses uniform random sampling. For dense graphs, our O(n 2.5/m) bound improves the best previously published bound by a factor of n 1/4 and a recent bound obtained independently of our work by a factor of logn. Our main insight is that graph search is wasteful when the graph is dense and can be avoided by searching the topological order space instead. Our algorithms extend to the maintenance of strong components, in the same asymptotic time bounds.

Incremental natural-gradient actor-critic algorithms

We present four new reinforcement learning algorithms based on actor-critic and natural-gradient ideas, and provide their convergence proofs. Actor-critic rein- forcement learning methods are online approximations to policy iteration in which the value-function parameters are estimated using temporal difference learning and the policy parameters are updated by stochastic gradient descent. Methods based on policy gradients in this way are of special interest because of their com- patibility with function approximation methods, which are needed to handle large or infinite state spaces. The use of temporal difference learning in this way is of interest because in many applications it dramatically reduces the variance of the gradient estimates. The use of the natural gradient is of interest because it can produce better conditioned parameterizations and has been shown to further re- duce variance in some cases. Our results extend prior two-timescale convergence results for actor-critic methods by Konda and Tsitsiklis by using temporal differ- ence learning in the actor and by incorporating natural gradients, and they extend prior empirical studies of natural actor-critic methods by Peters, Vijayakumar and Schaal by providing the first convergence proofs and the first fully incremental algorithms.