Implementation of Structural Assemblies by Simultaneous Projection and Density-Based Topology Optimization

This article proposed a methodology that combines two well-known projections and modified density-based optimized techniques in one formulation methodology. This methodology contains an effective explicit geometric entity identified by shape variables that provide easy control in desired particular regions; implicit density-based topological optimization entities utilized topological variables that offer critical design elsewhere. Our main attractive key point of this combined formulation approach is structural assemblies. Structure always manufactures in many patches and joins them by utilizing the structural assemblies such as welding and riveting. It is not easy to execute the structural patches at the required region without acknowledging their dimensions. This proposed approach demonstrates the competence to impose the restrictions related to shape and topological variables of interfaces among the specific patches. Numerous standard numerical examples make sure the validation of the introduced methodology. It remarked that the optimal design could minimize compliance and the minimum number of iterations through numerically performed, concerning computational cost minimized without any kind loss of accuracy of the final structure.

Non-Parametric Probability Distributions Embedded Inside of a Linear Space Provided with a Quadratic Metric

There exist uncertain situations in which a random event is not a measurable set, but it is a point of a linear space inside of which it is possible to study different random quantities characterized by non-parametric probability distributions. We show that if an event is not a measurable set then it is contained in a closed structure which is not a σ-algebra but a linear space over R. We think of probability as being a mass. It is really a mass with respect to problems of statistical sampling. It is a mass with respect to problems of social sciences. In particular, it is a mass with regard to economic situations studied by means of the subjective notion of utility. We are able to decompose a random quantity meant as a geometric entity inside of a metric space. It is also possible to decompose its prevision and variance inside of it. We show a quadratic metric in order to obtain the variance of a random quantity. The origin of the notion of variability is not standardized within this context. It always depends on the state of information and knowledge of an individual. We study different intrinsic properties of non-parametric probability distributions as well as of probabilistic indices summarizing them. We define the notion of α-distance between two non-parametric probability distributions.

Tuning of conic parameters using Tikhonov regularization and L-Curve simulation

In this article, a method to infer the parameters of a conic given a set of rectangular coordinates that belong to the geometric entity is shown. The methodology consists of solving a Tikhonov regulation problem where the unregulated term introduces the non-linear nature of the conical body and the regulated the restriction associated to the discriminant of the quadratic equation, then the solution is computed minimizing the resulting cost function where the Regularization parameter is tuned using the L-Curve technique. The model was validated with synthetic and real data from digital images, as well as subject to comparison against other state of the art alternatives. The results show that the method is robust against atypical values and the phenomenon of occlusion present in the data.

Aerodynamic Automobile Shape Optimization by Incorporating Reverse Shape Design Method With CFD Analysis

In modern automotive industry market, there have been a lot of state-of-art methodologies to perform a conceptual design of a car; functional methods and 3D scanning technology are widely used. Naturally, the issues frequently boiled down to a trade-off decision making problem between quality and cost. Besides, to incorporate the design method with advanced optimization methodologies such as design-of-experiments (DOE), surrogate modeling, how efficiently a method can morph or recreate a vehicle’s shape is crucial. This paper accomplishes an aerodynamic design optimization of rear shape of a sedan by incorporating a reverse shape design method (RSDM) with the aforementioned methodologies based on CFD analysis for aerodynamic drag reduction. RSDM reversely recovers a 3D geometry of a car from several 2D schematics. The backbone boundary lines of 2D schematic are identified and regressed by appropriate interpolation function and a 3D shape is yielded by a series of simple arithmetic calculations without losing the detail geometric features. Besides, RSDM can parametrize every geometric entity to efficiently manipulate the shape for application to design optimization studies. As the baseline, an Audi A6 is modeled by RSDM and explored through CFD analysis for model validation. Choosing six design variables around the rear shape, 77 design points are created to build neural networks. Finally, a significant amount of CD reduction is obtained and corresponding configuration is validated via CFD.

CHAIN-WISE GENERALIZATION OF ROAD NETWORKS USING MODEL SELECTION

Streets are essential entities of urban terrain and their automatized extraction from airborne sensor data is cumbersome because of a complex interplay of geometric, topological and semantic aspects. Given a binary image, representing the road class, centerlines of road segments are extracted by means of skeletonization. The focus of this paper lies in a well-reasoned representation of these segments by means of geometric primitives, such as straight line segments as well as circle and ellipse arcs. We propose the fusion of raw segments based on similarity criteria; the output of this process are the so-called chains which better match to the intuitive perception of what a street is. Further, we propose a two-step approach for chain-wise generalization. First, the chain is pre-segmented using <ttt>circlePeucker</ttt> and finally, model selection is used to decide whether two neighboring segments should be fused to a new geometric entity. Thereby, we consider both variance-covariance analysis of residuals and model complexity. The results on a complex data-set with many traffic roundabouts indicate the benefits of the proposed procedure.

Numerical simulation and experimental study on stress deformation of braided wire rope

To explore the mechanical properties of braided wire rope, relevant theories of differential geometry are applied to deduce the space curve parametric equation of braided wire rope, specific to the structural features of the rope. On this basis, a geometric entity model of YS9-8 × 19 braided wire rope is established. Through mesh generation, a finite element model of braided wire rope is obtained. Constraints and loads are applied for numerical simulation calculations. The numerical simulation results are analyzed to reveal the stress and deformation distribution rules of the rope strands along the rope axis direction and on the cross sections of strands. Tensile tests of YS9-8 × 19 steel wire ropes are performed. The test data and the analogous simulation results coincide, verifying the rationality of the model. The study provides theoretical bases for subsequent frictional wear and life studies on this steel wire rope.

Local Kinematic Analysis of Closed-Loop Linkages—Mobility, Singularities, and Shakiness

The mobility of a linkage is determined by the constraints imposed on its members. The geometric constraints define the configuration space (c-space) variety as the geometric entity in which the finite mobility of a linkage is encoded. The aim of a local kinematic analysis of a linkage is to deduce its finite mobility, in a given configuration, from the local c-space geometry. In this paper, a method for the local analysis is presented adopting the concept of the tangent cone to a variety. The latter is an algebraic variety approximating the c-space. It allows for investigating the mobility in regular as well as singular configurations. The instantaneous mobility is determined by the constraints, rather than by the c-space geometry. Shaky and underconstrained linkages are prominent examples that exhibit a permanently higher instantaneous than finite DOF even in regular configurations. Kinematic singularities, on the other hand, are reflected in a change of the instantaneous DOF. A c-space singularity as a kinematic singularity, but a kinematic singularity may be a regular point of the c-space. The presented method allows to identify c-space singularities. It also reveals the ith-order mobility and allows for a classification of linkages as overconstrained and underconstrained. The method is applicable to general multiloop linkages with lower pairs. It is computationally simple and only involves Lie brackets (screw products) of instantaneous joint screws. The paper also summarizes the relevant kinematic phenomena of linkages.

Local Analysis of Closed-Loop Linkages: Mobility, Singularities, and Shakiness

The mobility of a linkage is determined by the constraints imposed on its members. The constraints define the configuration space (c-space) variety as the geometric entity in which the finite mobility of a linkage is encoded. The instantaneous motions are determined by the constraints, rather than by the c-space geometry. Shaky linkages are prominent examples that exhibit a higher instantaneous than finite DOF even in regular configurations. Inextricably connected to the mobility are kinematic singularities that are reflected in a change of the instantaneous DOF. The local analysis of a linkage, aiming at determining the instantaneous and finite mobility in a given configuration, hence needs to consider the c-space geometry as well as the constraint system. A method for the local analysis is presented based on a higher-order local approximation of the c-space adopting the concept of the tangent cone to a variety. The latter is the best local approximation of the c-space in a general configuration. It thus allows for investigating the mobility in regular as well as singular configurations. Therewith the c-space is locally represented as an algebraic variety whose degree is the necessary approximation order. In regular configurations the tangent cone is the tangent space. The method is generally applicable and computationally simple. It allows for a classification of linkages as overconstrained and underconstrained, and to identify singularities.

An Abaqus Extension for 3-D Welding Simulations

An Abaqus Extension, in the form of an Abaqus/CAE Plug-In, is presented that enables an easy, efficient, model-tree based approach to setup all aspects of a welding model from within Abaqus/CAE. Specifically, the paper describes the extension to 3-D of a similar capability, namely the 2-D Abaqus Welding Interface (AWI), that currently exists for automating most of the repetitive, time-consuming tasks associated with building a welding model in a traditional CAE environment to facilitate weld simulations. The tasks supported by the 3-D AWI include weld-bead definitions based on simple cross-sectional geometric entity picks, options for geometry- or element-based bead-chunking in the weld direction, automatic definition of weld passes, steps and boundary conditions for each pass, and set-up of both the thermal and stress analysis models. The 3-D AWI is expected to make the normally time-consuming welding analysis setup significantly faster. The use of the AWI is demonstrated on a six-pass plate welding problem described in the literature.