Rotational Constraint between Beams in 3-D Space

In this paper, we develop two alternative formulations for the rotational constraint between the tangents to connected beams with large deformations in 3-D space. Such a formulation is useful for modeling bonded/welded connections between beams. The first formulation is derived by consistently linearizing the variation of the strain energy and by assuming linear shape functions for the beam elements. This formulation can be used with both the Lagrange multiplier and the penalty stiffness method. The second non-consistent formulation assumes that the contact normal is independent of the nodal displacements at each iteration, and is updated consistently between iterations. In other words, we ignore the contribution due to the change of the contact normal in the linearization of the contact gap function. This assumption yields simpler equations and requires no specific assumption regarding the shape functions for the underlying beam elements. However, it is limited to the penalty method. We demonstrate the performance of the presented formulations in solving problems using implicit time integration. We also present a case showing the implications of ignoring this rotational constraint in modeling a network of beams.</p

Підвищення енергоефективності комплекту розрядна лампа-ЕПРА

The network geometries of rigidly cross-linked fibrin and collagen type I networks are imaged using confocal microscopy and characterized statistically. This statistical representation allows for the regeneration of large, three-dimensional biopolymer networks using an inverse method. Finite element analyses with beam networks are then used to investigate the large deformation, nonlinear elastic response of these artificial networks in isotropic stretching and simple shear. For simple shear, we investigate the differential bulk modulus, which displays three regimes: a linear elastic regime dominated by filament bending, a regime of strain-stiffening associated with a transition from filament bending to stretching, and a regime of weaker strain-stiffening at large deformations, governed by filament stretching convolved with the geometrical nonlinearity of the simple shear strain tensor. The differential bulk modulus exhibits a corresponding strain-stiffening, but reaches a distinct plateau at about 5% strain under isotropic stretch conditions. The small-strain moduli, the bulk modulus in particular, show a significant size-dependence up to a network size of about 100 mesh sizes. The large-strain differential shear modulus and bulk modulus show very little size-dependence.Funding Agencies|BiMaC Innovation||Alf de Ruvo Memorial Foundation of SCA AB||WoodWisdom-net research program||Harvard MRSEC|DMR-0820484|NSF|DMR-1006546|</p

Characterization and impact of fiber size variability on the mechanical properties of fiber networks with an application to paper materials

Cellulose fibers come in a wide range of shapes and sizes. The heterogeneity of the fiber length, width, wall thickness, curl and external fibrillation is detrimental to the mechanical performance of products such as paper and paperboard. Although micro-mechanical models of these materials sometimes incorporate features of this heterogeneity, so far there is no standardized method of fully incorporating this. We examine a large number of industrial mechanical fiber pulps to determine what information such a standardized method would have to have. We find that the method must allow for both non-Gaussian distributions and dependence between the variables. We present a method of characterizing mechanical pulp under these conditions that views the individual fiber as outcome of a sampling process from a multivariate distribution function. The method is generally applicable to any dataset, even a non-Gaussian one with dependencies. Using a micro-mechanical model of a paper sheet the proposed method is compared with previously presented methods to study whether incorporating both a varying fiber size and dependencies is necessary to match the response of a sheet modeled with measured characterization data. The results demonstrate that micro-mechanical models of paper and paperboard should not neglect the influence of the dependence between the characteristic shape features of the fibers if the model is meant to match physical experiments. © 2022 The Author

Formation of Fuzzy Patterns in Logical Analysis of Data Using a Multi-Criteria Genetic Algorithm

The formation of patterns is one of the main stages in logical data analysis. Fuzzy approaches to pattern generation in logical analysis of data allow the pattern to cover not only objects of the target class, but also a certain proportion of objects of the opposite class. In this case, pattern search is an optimization problem with the maximum coverage of the target class as an objective function, and some allowed coverage of the opposite class as a constraint. We propose a more flexible and symmetric optimization model which does not impose a strict restriction on the pattern coverage of the opposite class observations. Instead, our model converts such a restriction (purity restriction) into an additional criterion. Both, coverage of the target class and the opposite class are two objective functions of the optimization problem. The search for a balance of these criteria is the essence of the proposed optimization method. We propose a modified evolutionary algorithm based on the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) to solve this problem. The new algorithm uses pattern formation as an approximation of the Pareto set and considers the solution&rsquo;s representation in logical analysis of data and the informativeness of patterns. We have tested our approach on two applied medical problems of classification under conditions of sample asymmetry: one class significantly dominated the other. The classification results were comparable and, in some cases, better than the results of commonly used machine learning algorithms in terms of accuracy, without losing the interpretability

Formation of Fuzzy Patterns in Logical Analysis of Data Using a Multi-Criteria Genetic Algorithm

The formation of patterns is one of the main stages in logical data analysis. Fuzzy approaches to pattern generation in logical analysis of data allow the pattern to cover not only objects of the target class, but also a certain proportion of objects of the opposite class. In this case, pattern search is an optimization problem with the maximum coverage of the target class as an objective function, and some allowed coverage of the opposite class as a constraint. We propose a more flexible and symmetric optimization model which does not impose a strict restriction on the pattern coverage of the opposite class observations. Instead, our model converts such a restriction (purity restriction) into an additional criterion. Both, coverage of the target class and the opposite class are two objective functions of the optimization problem. The search for a balance of these criteria is the essence of the proposed optimization method. We propose a modified evolutionary algorithm based on the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) to solve this problem. The new algorithm uses pattern formation as an approximation of the Pareto set and considers the solution’s representation in logical analysis of data and the informativeness of patterns. We have tested our approach on two applied medical problems of classification under conditions of sample asymmetry: one class significantly dominated the other. The classification results were comparable and, in some cases, better than the results of commonly used machine learning algorithms in terms of accuracy, without losing the interpretability