Nodal sensitivities as error estimates in computational mechanics

Summary This paper proposes the use of special sensitivities, called nodal sensitivities, as error indicators and estimators for numerical analysis in mechanics. Nodal sensitivities are defined as rates of change of response quantities with respect to nodal positions. Direct analytical differentiation is used to obtain the sensitivities, and the infinitesimal perturbations of the nodes are forced to lie along the elements. The idea proposed here can be used in conjunction with general purpose computational methods such as the Finite Element Method (FEM), the Boundary Element Method (BEM) or the Finite Difference Method (FDM); however, the BEM is the method of choice in this paper. The performance of the error indicators is evaluated through two numerical examples in linear elasticity.     

Kinetics of simultaneous two-phase precipitation in the Fe-C system

A theoretical approach for the interpretation of the kinetics of simultaneous stable and metastable phase precipitation in a binary system is proposed. The model, based on the nucleation and growth theory, defines a critical size different for each phase. The size of the clusters evolves by adding or substracting a single atom one at a time. A set of coupled differential equations is obtained for the chemical rate whose solution reproduces the kinetics of thermoelectric power measurements in the Fe-C multiphase system. Suppositions about the growing and dissolution rate constants reduce the size of the equation system with a gain in computation time.     

Node and element resequencing using the Laplacian of a finite element graph: Part I—General concepts and algorithm

A Finite Element Graph (FEG) is defined here as a nodal graph (G), a dual graph (G*), or a communication graph (G˙) associated with a generic finite element mesh. The Laplacian matrix ( L (G), L (G*) or L (G˙)), used for the study of spectral properties of an FEG, is constructed from usual vertex and edge connectivities of a graph. An automatic algorithm, based on spectral properties of an FEG (G, G* or G˙), is proposed to reorder the nodes and/or elements of the associated finite element mesh. The new algorithm is called Spectral PEG Resequencing (SFR). This algorithm uses global information in the graph, it does not depend on a pseudoperipheral vertex in the resequencing process, and it does not use any kind of level structure of the graph. Moreover, the SFR algorithm is of special advantage in computing environments with vector and parallel processing capabilities. Nodes or elements in the mesh can be reordered depending on the use of an adequate graph representation associated with the mesh. If G is used, then the nodes in the mesh are properly reordered for achieving profile and wavefront reduction of the finite element stiffness matrix. If either G* or G˙ is used, then the elements in the mesh are suitably reordered for a finite element frontai solver, A unified approach involving FEGs and finite element concepts is presented. Conclusions are inferred and possible extensions of this research are pointed out. In Part II of this work,¹ the computational implementation of the SFR algorithm is described and several numerical examples are presented. The examples emphasize important theoretical, numerical and practical aspects of the new resequencing method.     

T-stress in orthotropic functionally graded materials: Lekhnitskii and Stroh formalisms

A new interaction integral formulation is developed for evaluating the elastic T-stress for mixed-mode crack problems with arbitrarily oriented straight or curved cracks in orthotropic nonhomogeneous materials. The development includes both the Lekhnitskii and Stroh formalisms. The former is physical and relatively simple, and the latter is mathematically elegant. The gradation of orthotropic material properties is integrated into the element stiffness matrix using a “generalized isoparametric formulation” and (special) graded elements. The specific types of material gradation considered include exponential and hyperbolic-tangent functions, but micromechanics models can also be considered within the scope of the present formulation. This paper investigates several fracture problems to validate the proposed method and also provides numerical solutions, which can be used as benchmark results (e.g. investigation of fracture specimens). The accuracy of results is verified by comparison with analytical solutions.     

Indoor atmospheric corrosion in Cuba. A report about indoor localized corrosion

Indoor weight loss of steel, chloride, sulphur compounds and dust deposition rate were determined in six storehouses having different characteristics. Relative humidity and temperature were determined in three storehouses. A model for indoor corrosion of steel depending on time of exposure and deposition of dust, sulphur compounds and chlorides is proposed. Dust deposition plays an important role indoors. The position of the sample has also a significant influence on corrosion. Indoor corrosion aggressivity in Cuban storehouses ranges in classification IC3 and IC4 according to the new ISO proposal of indoor aggressivity.A report about the presence of localized corrosion indoors (filiform like) using a special designed sample is made.     

Superabsorbent hydrogel based on modified polysaccharide for removal of Pb2+ and Cu2+ from water with excellent performance

This contribution describes the absorption percentage of Pb²⁺ and Cu²⁺ from water by a superabsorbent hydrogel matrix (SH) made from an anionic polysaccharide copolymerized with acrylic acid (AAc) and acrylamide (AAm). Metal‐absorption tests, upon sequential pH variation, indicated that the SH has pH‐sensitivity for the absorption of both metals from solution, attributed to the functional ionic groups (? COOH) present in the AAc and arabic gum (AG) segments. At the pH 5.0, the SH exhibited good absorption capacity: 73.10% for Pb²⁺, 81.99% for Cu²⁺ in water and 63.64% for Pb²⁺, and 76.67% for Cu²⁺ in saline water with 0.1 mol kg^?1 ionic strength. A replicated 2² full factorial design with a central point was built to evaluate the maximum absorption capacity of the metals into the SH. It was found that both the interaction and main effects of the pH and the initial concentration of metal solution on absorption percentage of the metals were statistically significant. Surface response plots indicated that the absorption capacity of both metals into the SH may be appreciably improved by using the solutions with lower initial concentration of metal and with higher pH values. Metal‐absorption results demonstrated that the SH is a convenient material for absorption of Pb²⁺ and Cu²⁺ from pure aqueous and saline aqueous environments. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007     

A New Geometric Subproblem to Extend Solvability of Inverse Kinematics Based on Screw Theory for 6R Robot Manipulators

Geometric inverse kinematics procedures that divide the whole problem into several subproblems with known solutions, and make use of screw motion operators have been developed in the past for 6R robot manipulators. These geometric procedures are widely used because the solutions of the subproblems are geometrically meaningful and numerically stable. Nonetheless, the existing subproblems limit the types of 6R robot structural configurations for which the inverse kinematics can be solved. This work presents the solution of a novel geometric subproblem that solves the joint angles of a general anthropomorphic arm. Using this new subproblem, an inverse kinematics procedure is derived which is applicable to a wider range of 6R robot manipulators. The inverse kinematics of a closed curve were carried out, in both simulations and experiments, to validate computational cost and realizability of the proposed approach. Multiple 6R robot manipulators with different structural configurations were used to validate the generality of the method. The results are compared with those of other methods in the screw theory framework. The obtained results show that our approach is the most general and the most efficient.

     

Polygonal multiresolution topology optimization (PolyMTOP) for structural dynamics

We use versatile polygonal elements along with a multiresolution scheme for topology optimization to achieve computationally efficient and high resolution designs for structural dynamics problems. The multiresolution scheme uses a coarse finite element mesh to perform the analysis, a fine design variable mesh for the optimization and a fine density variable mesh to represent the material distribution. The finite element discretization employs a conforming finite element mesh. The design variable and density discretizations employ either matching or non-matching grids to provide a finer discretization for the density and design variables. Examples are shown for the optimization of structural eigenfrequencies and forced vibration problems.     

Honeycomb Wachspress finite elements for structural topology optimization

Traditionally, standard Lagrangian-type finite elements, such as linear quads and triangles, have been the elements of choice in the field of topology optimization. However, finite element meshes with these conventional elements exhibit the well-known “checkerboard” pathology in the iterative solution of topology optimization problems. A feasible alternative to eliminate such long-standing problem consists of using hexagonal (honeycomb) elements with Wachspress-type shape functions. The features of the hexagonal mesh include two-node connections (i.e. two elements are either not connected or connected by two nodes), and three edge-based symmetry lines per element. In contrast, quads can display one-node connections, which can lead to checkerboard; and only have two edge-based symmetry lines. In addition, Wachspress rational shape functions satisfy the partition of unity condition and lead to conforming finite element approximations. We explore the Wachspress-type hexagonal elements and present their implementation using three approaches for topology optimization: element-based, continuous approximation of material distribution, and minimum length-scale through projection functions. Examples are presented that demonstrate the advantages of the proposed element in achieving checkerboard-free solutions and avoiding spurious fine-scale patterns from the design optimization process.