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Displacement: Translation and Rotation. Differences and Similarities in the Discrete and Continuous Models
104-124Views:116The motion (displacement) of the Euclidean space can be decomposed into translation and rotation. The two kinds of motion of the Euclidean space based on two structures of the Euclidean space: The first one is the topological structure, the second one is the idea of distance. The motion is such a (topological) map, that the distance of any two points remains the same. The bounded and closed domain of the Euclidean space is taken as a model of the rigid body. The bounded and closed domain of the Euclidean space is also taken as a model of the deformable solid body. The map – i.e. the displacement field – of the deformable solid body is continuous, but is not (necessarily) motion; the size and the shape of body can change. The material has atomic-molecular structure. In compliance with it, the material can be comprehended as a discrete system. In this case the elements of the material, as an atom, molecule, grain, can be comprehended as either material point, or rigid body. In the first case the kinematical freedom is the translation, in the latter case the translation and the rotation. In the paper we analyse how the kinematical behaviour of the discrete and continuous mechanical system can be characterise by translation and rotation. In the discrete system the two motions are independent variable. At the same time they characterise the movement of the body different way. For instance homogeneous local translation gives the global translation, but the homogeneous local rotation does not give the global rotation. To realise global rotation in a discrete system on one hand global rotation of the position of the discrete elements, on the other hand homogeneous local rotations of the discrete elements in harmony with global rotation are required. In the continuous system the two kinds of movement cannot be interpreted: a point cannot rotate, a rotation of surrounding of a point or direction can be interpreted. The kinematical characteristics, as the displacement (practically this is equal to translation) of (neighbourhood of) point, the rotation of surrounding of that point and the rotation of a direction went through that point are not independent variables: the translation of a point determines the rotation of the surrounding of that point as well as the rotation of a direction went through that point. With accordance this statement the displacement (practically translation) (field) as the only kinematical variable can be interpreted in the continuous medium.
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The Possible Job Creation and Job Destructive Effects of Technological Development
53-61Views:297Throughout history, technological change has often provided the basis for employee anxiety. Between 1811 and 1816, a group of workers in England who called themselves "Luddists" destroyed machines, because they thought it would endanger their workplace. 19th-century thinkers and economists such as Karl Marx and David Ricardo predicted that mechanizing the economy would ultimately worsen workers' conditions, depriving them of a decent wage. Over the last century, John M. Keynes (1930s) and Wassily Leontief (1950s) have expressed their fears that more and more workers will be replaced by machine solutions that will lead to unemployment. In recent years, Brynjolfsson and McAfee (2014) have argued that existing technologies reduce the demand for labor and put some of the human workforce at a permanent disadvantage. However, there are a number of compensation mechanisms that can offset the initial displacement effects of automation and process innovation in general (Vivarelli, 2015). First of all, while workers are being replaced in industries that introduce new machine technology, additional workers in new industries are needed. Second, automation (and process innovation in general) reduces average costs. Acemoglu and Restrepo (2017) found that this results, on the one hand, in the effect of price productivity (“priceproductivity”) (as production costs decrease, the industry can expand and increase labor demand); and, on the other hand, it leads to economies of scale in production (the reduction in costs due to automation leads to an increase in total output and increases the demand for labor in all industries). Similarly, Vivarelli (2015) argues that lower average costs can result in lower prices (if the industry's market structure is perfectly competitive), stimulate product demand, or result in extra profits (if the industry's structure is not perfectly competitive). If these extra profits are reinvested in the company, this investment can create new jobs. The presentation intends to present these counterbalancing cases and to provide real examples based on the literature.
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An Analytical Solution for the Two-Layered Composite Beam-Column with Interlayer Slip and Constant Axial Load
14-31Views:45The authors present an analytical solution for the two-layered composite beams with imperfect shear connections. The considered beam is simply supported at both ends. The beam is subjected to transverse and axial loads. The kinematic assumptions of the Euler-Bernoulli beam theory are used. The connection of the beam components is perfect in normal direction, but the axial displacement field may have jump. The shear axial force derived from the imperfect connection is proportional to the relative slip occurring between the layers. The determination of the analytical solution is based on the Fourier method. Two examples illustrate the application of the presented analytical method.
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Optimization of the Sheet Metal Base of a Toggle Clamp Using Finite Element Method
266-273Views:184Optimization relates to the ultimate yield strength and the maximum stress incident on the current model under critical working conditions and finds through iterative processing a way to compensate for the strength requirement without going beyond the desired mass limits. In this paper, the horizontal sheet metal base of a horizontal toggle clamp is optimised for mass reduction using the finite element analysis in the computer aided design software. The sheet metal base material is the ANSI32 Steel. In the design software, it is designed with the thickness of 7 mm and it is intended to support a workload of up to 750 N. The constraints were a fixed point added at all the holes and at the bottom surface of the sheet metal base. A number of iterations were made for the 750N loading force across the base plate to run the simulation. For optimization, the aim was to minimize the mass of the base plate. The design parameters were Von Mises, factor of safety and displacement. The variables were the slots’ width and material thickness along the mid-surface of the sheet metal. The mass was reduced by more than thirty per cent overall.
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Topology Optimization of Automotive sheet metal part using Altair Inspire
143-150Views:716In an optimization problem, different candidate solutions are compared with each other, and then the best or optimal solution is obtained which means that solution quality is fundamental. Topology optimization is used at the concept stage of design. It deals with the optimal distribution of material within the structure. Altair Inspire software is the industry's most powerful and easy-to-use Generative Design/Topology Optimization and rapid simulation solution for design engineers. In this paper Topology optimization is applied using Altair inspire to optimize the Sheet metal Angle bracket. Different results are conducted the better and final results are fulfilling the goal of the paper which is minimizing the mass of the sheet metal part by 65.9% part and Maximizing the stiffness with Better Results of Von- Miss Stress Analysis, Displacement, and comparison with different load cases. This can lead to reduced costs, development time, material consumption, and product less weight.
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Neutral Inhomogeneity in Circular Cylinder Subjected to Axial Load on its Lateral Boundary
35-42Views:132In this paper we consider the problem of single circular elastic inhomogeneity embedded within a circular cylinder whose curved boundary surface is subjected to surface traction acting on axial direction. We investigate the displacement neutrality of the coupled system of host body and inclusion. Neutral inhomogeneity (inclusion) does not disturb the displacement, strain and stress fields in the host body. The deformation of the considered inhomogenneous cylinder is antiplane shear deformation.
