Wave propagation in fiber composite laminates, part 2

An experimental investigation was conducted to determine the wave propagation characteristics, transient strains and residual properties in unidirectional and angle-ply boron/epoxy and graphite/epoxy laminates impacted with silicone rubber projectiles at velocities up to 250 MS-1. The predominant wave is flexural, propagating at different velocities in different directions. In general, measured wave velocities were higher than theoretically predicted values. The amplitude of the in-plane wave is less than ten percent of that of the flexural wave. Peak strains and strain rates in the transverse to the (outer) fiber direction are much higher than those in the direction of the fibers. The dynamics of impact were also studied with high speed photography

A second derivative SQP method: theoretical issues

Sequential quadratic programming (SQP) methods form a class of highly efficient algorithms for solving nonlinearly constrained optimization problems. Although second derivative information may often be calculated, there is little practical theory that justifies exact-Hessian SQP methods. In particular, the resulting quadratic programming (QP) subproblems are often nonconvex, and thus finding their global solutions may be computationally nonviable. This paper presents a second-derivative SQP method based on quadratic subproblems that are either convex, and thus may be solved efficiently, or need not be solved globally. Additionally, an explicit descent-constraint is imposed on certain QP subproblems, which “guides” the iterates through areas in which nonconvexity is a concern. Global convergence of the resulting algorithm is established

Lamination residual stresses in hybrid composites, part 1

An experimental investigation was conducted to study lamination residual stresses for various material and loading parameters. The effects of hybridization on residual stresses and residual properties after thermal cycling under load were determined in angle-ply graphite/Kevlar/epoxy and graphite/S-glass/epoxy laminates. Residual strains in the graphite plies are not appreciably affected by the type and number of hybridizing plies. Computed residual stresses at room temperature in the S-glass plies reach values up to seventy-five percent of the transverse strength of the material. Computed residual stresses in the graphite plies exceed the static strength by approximately ten percent. In the case of Kevlar plies, computed residual stresses far exceed the static strength indicating possible early failure of these plies. Static testing of the hybrids above indicates that failure is governed by the ultimate strain of the graphite plies. In thermally cycled hybrids, in general, residual moduli were somewhat lower and residual strengths were higher than initial values

Lamination residual stresses in fiber composites

An experimental investigation was conducted to determine the magnitude of lamination residual stresses in angle-ply composites and to evaluate their effects on composite structural integrity. The materials investigated were boron/epoxy, boron/polyimide, graphite/low modulus epoxy, graphite/high modulus epoxy, graphite/polyimide and s-glass/epoxy. These materials were fully characterized. Static properties of laminates were also determined. Experimental techniques using embedded strain gages were developed and used to measure residual strains during curing. The extent of relaxation of lamination residual stresses was investigated. It was concluded that the degree of such relaxation is low. The behavior of angle-ply laminates subjected to thermal cycling, tensile load cycling, and combined thermal cycling with tensile load was investigated. In most cases these cycling programs did not have any measurable influence on residual strength and stiffness of the laminates. In the tensile load cycling tests, the graphite/polyimide shows the highest endurance with 10 million cycle runouts at loads up to 90 percent of the static strength

Electronic and thermoelectric properties of Fe2VAl: The role of defects and disorder

Using first-principles calculations, we show that Fe2VAl is an indirect band gap semiconductor. Our calculations reveal that its, sometimes assigned, semimetallic character is not an intrinsic property but originates from the antisite defects and site disorder, which introduce localized ingap and resonant states changing the electronic properties close to band gap. These states negatively affect the thermopower S and power factor PF=S^2\sigma, decreasing the good thermoelectric performance of intrinsic Fe2VAl.Comment: 4 pages, 6 figures, thermoelectric properties, electronic structure and transport properties, effect of antisite defects and disorder on electronic and transport propertie

A second derivative SQP method: local convergence

In [19], we gave global convergence results for a second-derivative SQP method for minimizing the exact ℓ1-merit function for a fixed value of the penalty parameter. To establish this result, we used the properties of the so-called Cauchy step, which was itself computed from the so-called predictor step. In addition, we allowed for the computation of a variety of (optional) SQP steps that were intended to improve the efficiency of the algorithm. \ud \ud Although we established global convergence of the algorithm, we did not discuss certain aspects that are critical when developing software capable of solving general optimization problems. In particular, we must have strategies for updating the penalty parameter and better techniques for defining the positive-definite matrix Bk used in computing the predictor step. In this paper we address both of these issues. We consider two techniques for defining the positive-definite matrix Bk—a simple diagonal approximation and a more sophisticated limited-memory BFGS update. We also analyze a strategy for updating the penalty paramter based on approximately minimizing the ℓ1-penalty function over a sequence of increasing values of the penalty parameter.\ud \ud Algorithms based on exact penalty functions have certain desirable properties. To be practical, however, these algorithms must be guaranteed to avoid the so-called Maratos effect. We show that a nonmonotone varient of our algorithm avoids this phenomenon and, therefore, results in asymptotically superlinear local convergence; this is verified by preliminary numerical results on the Hock and Shittkowski test set

A second-derivative trust-region SQP method with a "trust-region-free" predictor step

In (NAR 08/18 and 08/21, Oxford University Computing Laboratory, 2008) we introduced a second-derivative SQP method (S2QP) for solving nonlinear nonconvex optimization problems. We proved that the method is globally convergent and locally superlinearly convergent under standard assumptions. A critical component of the algorithm is the so-called predictor step, which is computed from a strictly convex quadratic program with a trust-region constraint. This step is essential for proving global convergence, but its propensity to identify the optimal active set is Paramount for recovering fast local convergence. Thus the global and local efficiency of the method is intimately coupled with the quality of the predictor step.\ud \ud In this paper we study the effects of removing the trust-region constraint from the computation of the predictor step; this is reasonable since the resulting problem is still strictly convex and thus well-defined. Although this is an interesting theoretical question, our motivation is based on practicality. Our preliminary numerical experience with S2QP indicates that the trust-region constraint occasionally degrades the quality of the predictor step and diminishes its ability to correctly identify the optimal active set. Moreover, removal of the trust-region constraint allows for re-use of the predictor step over a sequence of failed iterations thus reducing computation. We show that the modified algorithm remains globally convergent and preserves local superlinear convergence provided a nonmonotone strategy is incorporated

A model balancing cooperation and competition explains our right-handed world and the dominance of left-handed athletes

An overwhelming majority of humans are right-handed. Numerous explanations for individual handedness have been proposed, but this population-level handedness remains puzzling. Here we use a minimal mathematical model to explain this population-level hand preference as an evolved balance between cooperative and competitive pressures in human evolutionary history. We use selection of elite athletes as a test-bed for our evolutionary model and account for the surprising distribution of handedness in many professional sports. Our model predicts strong lateralization in social species with limited combative interaction, and elucidates the rarity of compelling evidence for "pawedness" in the animal world.Comment: 5 pages of text and 3 figures in manuscript, 8 pages of text and two figures in supplementary materia