Use of arc-length method for capturing mode jumping in postbuckling aerostructures

The arc-length method has become a widely established solution technique for studying nonlinear structural behavior. By augmenting the set of nonlinear equilibrium equations with a constraint equation, which is a function of both the displacements and load increment, it is capable of traversing limit points. Numerous investigations have shown that highly nonlinear behavior such as sharp "snap-backs" can still lead to numerical difficulties. Two practical examples are presented to assess the effectiveness of this solution technique in capturing secondary instabilities in postbuckling structures, which present themselves as abrupt mode jumps. Although the first example poses no special difficulties, in the second case the nonlinear procedure fails to converge. An improvement to the method's formulation is suggested, which accounts for the residual forces that are usually neglected, when proceeding to the next increment once convergence is reached on the current increment. The choice of a correct load increment at the first iteration, within a predictor-corrector scheme, is central to the method's effectiveness. Current strategies for a choice of this load increment are discussed and are shown to be no longer consistent with the modified formulation; therefore, a new approach is proposed.

Factorial Design of Cement Slurries Containing Limestone Powder for Self-Consolidating Slurry-Infiltrated Fiber Concrete

Slurries with high penetrability for production of Self-consolidating Slurry Infiltrated Fiber Concrete (SIFCON) were investigated in this study. Factorial experimental design was adopted in this investigation to assess the combined effects of five independent variables on mini-slump test, plate cohesion meter, induced bleeding test, J-fiber penetration test and compressive strength at 7 and 28 days. The independent variables investigated were the proportions of limestone powder (LSP) and sand, the dosages of superplasticiser (SP) and viscosity agent (VA), and water-to-binder ratio (w/b). A two-level fractional factorial statistical method was used to model the influence of key parameters on properties affecting the behaviour of fresh cement slurry and compressive strength. The models are valid for mixes with 10 to 50% LSP as replacement of cement, 0.02 to 0.06% VA by mass of cement, 0.6 to 1.2% SP and 50 to 150% sand (% mass of binder) and 0.42 to 0.48 w/b. The influences of LSP, SP, VA, sand and W/B were characterised and analysed using polynomial regression which identifies the primary factors and their interactions on the measured properties. Mathematical polynomials were developed for mini-slump, plate cohesion meter, J-fiber penetration test, induced bleeding and compressive strength as functions of LSP, SP, VA, sand and w/b. The estimated results of mini-slump, induced bleeding test and compressive strength from the derived models are compared with results obtained from previously proposed models that were developed for cement paste. The proposed response models of the self-consolidating SIFCON offer useful information regarding the mix optimization to secure a highly penetration of slurry with low compressive strength

White matter fractional anisotrophy predicts balance performance in older adults

Aging is characterized by brain structural changes that may compromise motor functions. In the context of postural control, white matter integrity is crucial for the efficient transfer of visual, proprioceptive and vestibular feedback in the brain. To determine the role of age-related white matter decline as a function of the sensory feedback necessary to correct posture, we acquired diffusion weighted images in young and old subjects. A force platform was used to measure changes in body posture under conditions of compromised proprioceptive and/or visual feedback. In the young group, no significant brain structure-balance relations were found. In the elderly however, the integrity of a cluster in the frontal forceps explained 21% of the variance in postural control when proprioceptive information was compromised. Additionally, when only the vestibular system supplied reliable information, the occipital forceps was the best predictor of balance performance (42%). Age-related white matter decline may thus be predictive of balance performance in the elderly when sensory systems start to degrade.

The Reliability of the Arc-Length Method in the Analysis of Mode-Jumping Problems

The Arc-Length Method is a solution procedure that enables a generic non-linear problem to pass limit points. Some examples are provided of mode-jumping problems solutions using a commercial nite element package, and other investigations are carried out on a simple structure of which the numerical solution can be compared with an analytical one. It is shown that Arc-Length Method is not reliable when bifurcations are present in the primary equilibrium path; also the presence of very sharp snap-backs or special boundary conditions may cause convergence diÆculty at limit points. An improvement to the predictor used in the incremental procedure is suggested, together with a reliable criteria for selecting either solution of the quadratic arc-length constraint. The gap that is sometimes observed between the experimantal load level of mode-jumping and its arc-length prediction is explained through an example.