Two-level mathematical models for determining the stress state and life plate with a hole

Modern trends in the development of mechanical engineering and other industries related to the production of materials and structures with a given set of physical, mechanical, and technological properties are aimed at reducing material consumption, energy consumption, increasing accuracy, reliability, and competitiveness of the manufactured product. Therefore, the creation of mathematical methods for assessing the stress state of structural elements based on the analysis of the elastic characteristics of a material, taking into account the peculiarities of its internal microstructure, is an actual task. The considered algorithm includes the following stages: identification of strength parameters using data obtained from images of the material microstructure; study of the stress-strain state of the model based on the variational-difference finite element method; formation of a system of linear algebraic equations for solving the problem of analyzing the elastic properties of a material using the plane problem of the theory of elasticity; construction of the material yield surface for a series of tests based on the strength criteria of composite materials, taking into account the different resistance of the material under tensile and compressive loads. Based on the developed mathematical model, the SSS and the yield surface of the plate with a hole are estimated. Structural analysis is performed at the macro and micro levels. The occurrence of plastic deformations at the micro-level can lead to the development of cracks and structural damage at the macro level. As a result of the study, the probability of plastic deformation in the plate is determined, and the critical zones of the model are established. The practical significance of the results obtained is to create an approach to assessing the mechanical properties of a material, such as elastic modulus, shear modulus, Poisson's ratio, and their probabilistic characteristics following the internal material structure. The proposed approach contributes to the expansion of knowledge about the material and allows to increase the valuable information obtained by modeling. To assess the probability of plastic deformations, the generated method uses the entire set of probabilistic characteristics of the yield surface.

CONTACT INTERACTION OF A TORSION SHAFT WITH A SPLINED BUSH IN ELASTICALLY PLASTIC DEFORMATIONS

Torsion shafts are the main elastic element of the suspension systems of a large number of vehicles. To simulate their reaction to the action of torque, the stress-strain state is analyzed taking into account the contact interaction with the spline sleeve. The features of the distribution of contact pressure between these bodies are established. The nature of stress concentration in the splined hollows of the shaft head is determined. Models and research methods have been developed that make it possible to develop recommendations for design decisions in the design of vehicle suspension systems. The factors are determined that ensure the strength of the torsion shaft at the values of its head diameters close to the diameters of the torsion shaft stem. In the case under consideration, this factor is firstly strength of the torsion shaft head. In particular, it was found that during manufacturing operations there are significant plastic deformations and contact loads in the heads of torsion shafts. This factor is decisive in substantiating the design parameters of torsion shafts. Keywords: torsion shaft; contact interaction; stress-strain state; elastically plastic deformation; suspension system

Fresh Properties and Mix Design for 3D-Printable Decorative Concrete

Постановка задачи. Рассмотрение закономерностей влияния вида цемента и модификаторов вязкости на технологические свойства смесей для 3D-печати определяется необходимостью одновременного обеспечения показателей пластичности и формоустойчивости смесей и декоративности композитов на их основе. Результаты. Представлены результтаты экспериментальных исследований основных реологических характеристик декоративного бетона для строительной 3D-печати. Выявлено влияние состава бетона на подвижность и формоустойчивость смеси. Установлено, что вид используемого цемента изменяет пластичность смеси и формоустойчивость под весом вышележащих слоев. Смеси с оптимальным компонентным составом декоративного бетона для строительной 3D-печати имеют следующие реологические характеристики: предел текучести K @ 1,0-2,2 кПа, структурная прочность s = 1,5-4,5 кПа, относительные пластические деформации Δ = 0,03-0,07 мм/мм. Данные характеристики определяют способность смеси к пластическому деформированию без разрушения структуры при течении, а также способность сохранять форму при печати слоя и нагружении вышележащими слоями. Выводы. Оптимальные диапазоны свойств смесей для 3D-печати могут быть изменены в 2-3 раза за счет использования цементов с различным гранулометрическим составом. Регулирование подвижности и формоустойчивости смесей с различными видами цемента главным образом обеспечивается применяемым модификатором вязкости. Statement of the problem. This paper present the rheological properties of 3D-printable decorative concrete. The effects of the mix proportion on its plasticity and shape stability are presented together. It has been established that a kind of cement changes the plasticity of fresh mixtures and its resistance to load during printing. Results. The fresh mixtures of 3D-printable decorative concrete with effective mix design had plastic yield value K @ 1.0-2.2 kPa, structural strength s = 1.5-4.5 kPa, value of plastic deformations Δ = 0.03-0.07 mm/mm. That has defined the ability of these mixes to plastically deform without any structure destruction and hold its shape, resist the deformation under compressions load during multi-layer casting. Conclusions. Shape stability of 3D-printable mix can be changed by 2-3 times by using cement with an efficient ranging of a particle size. The plasticity and shape stability of fresh mixes can be regulated using viscosity modifiers whose type depends on the type of cement.

Application of a finite deformation multiplicative plasticity model with non-local hardening to the simulation of CPTu tests in a structured soil

In this paper an isotropic hardening elastoplastic constitutive model for structured soils is applied to the simulation of a standard CPTu test in a saturated soft structured clay. To allow for the extreme deformations experienced by the soil during the penetration process, the model is formulated in a fully geometric non-linear setting, based on: i) the multiplicative decomposition of the deformation gradient into an elastic and a plastic part; and, ii) on the existence of a free energy function to define the elastic behaviour of the soil. The model is equipped with two bonding-related internal variables which provide a macroscopic description of the effects of clay structure. Suitable hardening laws are employed to describe the structure degradation associated to plastic deformations. The strain-softening associated to bond degradation usually leads to strain localization and consequent formation of shear bands, whose thickness is dependent on the characteristics of the microstructure (e.g, the average grain size). Standard local constitutive models are incapable of correctly capturing this phenomenon due to the lack of an internal length scale. To overcome this limitation, the model is framed using a non-local approach by adopting volume averaged values for the internal state variables. The size of the neighbourhood over which the averaging is performed (characteristic length) is a material constant related to the microstructure which controls the shear band thickness. This extension of the model has proven effective in regularizing the pathological mesh dependence of classical finite element solutions in the post-localization regime. The results of numerical simulations, conducted for different soil permeabilities and bond strengths, show that the model captures the development of plastic deformations induced by the advancement of the cone tip; the destructuration of the clay associated with such plastic deformations; the space and time evolution of pore water pressure as the cone tip advances. The possibility of modelling the CPTu tests in a rational and computationally efficient way opens a promising new perspective for their interpretation in geotechnical site investigations.

Analysis of Interference-Fit Joints

Interference fit joints have been widely used in many engineering constructions, in particular in electric motors. It is of particular importance to calculate the load capacity of press-fit joints, especially in the overload ranges of construction to estimate the safety factor. The article presents a FEM numerical simulation of pressing the shaft into the hub, taking into account various types of fits. The results of numerical simulations presented in the article were positively verified with the MTS measuring device, which confirmed the correctness of the numerical model. So far, the load-bearing capacity of press-fit joints has been calculated from Lame’s formulas. The results of the load capacity of the joints obtained by the FEM simulation were compared with the results obtained from Lame’s formula. The comparison shows that when designing interference fit joints, attention should be paid to the fact that the press-in process, depending on the type of fit, may be elastic-plastic. Plastic deformations in the contact zone of the joint affect its load-bearing capacity. Therefore, the design of press-fit joints should not be based on Lame’s formulas, which do not take into account the range of plastic work of the material.

Approximate methods for calculating the impact of a massive body on a plate lying on the base

Normal impact of a massive body on a uniformly stretched plate lying on the base is investigated. A hinged round or rectangular plate on an elastic base, or an infinite plate on the surface of an ideal incompressible fluid is considered. The solution to the elastoplastic impact is in good agreement with numerical calculations and experimental data. With a small parameter of elastic collapse, that is, with the developed local plastic deformations, a solution to the problem of impact with rigid-plastic local collapse can be used. Approximate formulas for calculating the main characteristics of rigid-plastic impact are set up.

FRESH PROPERTIES AND MIX DESIGN FOR 3D-PRINTABLE DECORATIVE CONCRETE

Statement of the problem. This paper present the rheological properties of 3D-printable decorative concrete. The effects of mix proportion on its plasticity and shape stability are presented together. It has been established that kind of cement changes plasticity of fresh mixtures and its resistance to load during the printing. Results. The fresh mixtures of 3D-printable decorative concrete with effective mix design had plastic yield value Ki 1.0 - 2.2 kPa, structural strength σ0 = 1.5 - 4.5 kPa, value of plastic deformations Δpl = 0.03 - 0.07 mm/mm. That is defined the ability of these mixtures to plastically deform without structure destruction and hold its shape, resist the deformation under compressions load during multi-layer casting.Conclusions. Shape stability of 3D-printable mixture can be changed by 2--3 times by using cement with efficient ranging of a particle size. The plasticity and shape stability of fresh mixtures can be regulated with usage of viscosity modifiers, the type of which depends on the type of cement.