Papers by Keyword: Hooke's Law

Abstract: In connection with the development of 3D printing and expanding the possibilities of implementing 3D printing outputs in technology and industry, there is a growing need to know the properties of printed products during their mechanical stress depending on their internal structure, temperature, static and cyclic mechanical stress. The subject of the contribution is the development and construction of precise testing equipment for 3D printing products, such as plastics as well as metallic and non-metallic samples up to the level of force acting on samples with a maximum value of 5 kN. The test device is designed as a bench-top laboratory device, consisting of a linear carriage guide for fixing the sample, a helix driven through a planetary gearbox by a hybrid stepper motor with a rotary encoder. The transmission ratio of the gearbox is 1:50, the resolution of the rotary encoder is adjustable up to a value of 50000 steps per one revolution of the motor. The carriages for fixing the sample are printed by 3D printing from a material with the addition of carbon fibers. The device includes a dynamometer with a range of ± 5 kN for accurate measurement of the forces acting on the samples. The device is primarily intended for tensile stressing of samples in a limited range, which is determined by the type and method of holding the sample. It is also possible to implement pressure stressing. Control of the test equipment is realized using a 32-bit microcontroller of the ARM Cortex class of the STM32L476 type series. Control has two basic modes: manual and program controlled. In manual mode, it is possible to control the displacement speed continuously or in steps in both directions by means of the rotary encoder, buttons and display for setting and fixing the tested sample. In the program mode, it is possible to control the test device via the USB interface from the host computer. In addition to controlling the stepper motor, the device also includes an external 24-bit ADC converter for the dynamometer, an interface for connecting 1-wire thermometers, sensing the status of safety limit switches and, in the future, also controlling the temperature chamber. Test procedures and material tests can be programmed and interactively managed using the Python language in the Jupyter-Lab environment, thus automating the implementation of test procedures. The test outputs are data in files and also in generated graphs in the Jupyter environment. Elementary basic calculations related to test procedures are also performed in the Jupyter environment, such as calculation of energy by area integration, Young's modulus, etc. The testing device enables tensile tests to be carried out according to the EN ISO 52 standard.

Abstract: This paper establishes two-dimensional mathematical model and three-dimensional mathematical model of the mechanical structure elastic-plastic mechanics and according to Hooke's law and Drucker postulate analyzes the plastic relationship of the elastic-plastic mechanics. The first part of the paper introduces the parameter setting of finite element analysis of elastic-plastic mechanics. The second part establishes computer simulation model of elastoplastic. Finally, it analyzes bolt force using ANSYS software and applies it to computer simulation of elastoplastic force and air resistance of gymnast in the process of action showing which provides technical reference for the training of gymnasts.

Abstract: Based on the generalized Hooke's law and the superposition principle, a new element model of linearly elastic and orthotropic solid bodies is presented. Furthermore, the paper provides a new method for analyzing solid bodies. This new element is a simple truss, and a solid body is considered to consist of many such truss elements, then the solid body becomes a truss structure. Thus the internal forces and displacements of the solid body can be obtained by calculating this truss structure.