Non-axisymmetric Loading Research Articles

Связанная неосесимметричная нестационарная задача термоупругости для длинного цилиндра

Inhomogeneous non-stationary heating of constructions of various purposes induces thermal strains and stresses that should be considered in the comprehensive analysis of elastic systems. The mathematical formulation of the considered linear threedimensional thermoelasticity problems includes coupled non-self-adjoint differential equations of motion and thermal conductivity. Due to their integration difficulty, axisymmetric problems are usually analyzed instead. The purpose of this work is to develop a solution algorithm for the coupled nonaxisymmetric non-stationary problem of the thermoelasticity of a long cylinder. On the internal surface of the hollow anisotropic cylinder, the temperature variation function is known; on the external surface, the convective heat transfer and environmental temperature are given. The rate of the temperature load does not affect the inertial characteristics of the cylinder. Therefore, the equilibrium and heat equations can be added to the initial system of linear equations. The finite Fourier sine and cosine transforms and general biorthogonal transforms are used to study a non-self-adjoint system of differential equations and to develop a closed solution. The obtained solution allows one to determine the temperature field and the stress-strain state of a cylinder with its internal surface affected by non-stationary nonaxisymmetric loading in terms of the temperature variation function.

The non-axisymmetric loading of an elastoplastic three-layer plate in its plane

The statement of the boundary value problem on the deformation of a circular three-layer plate in its plane under the action of a non-axisymmetric load is herein presented. The materials of thin carrier layers obey the hypotheses of the theory of small elastoplastic deformations. The relatively thick filler is physically non-linearly elastic. A system of non-linear differential equilibrium equations in partial derivatives is obtained. A general technique for solving the problem in displacements based on the Fourier method and Ilyushin’s method of elastic solutions is proposed. The case of an external cosine load is considered. An iterative solution of a boundary value problem for a physically non-linear plate is obtained. The corresponding solution of the elastic problem is written out in the final form. The obtained solution is numerically tested.

A crystal plasticity model for porous HCP crystals in titanium alloys under multiaxial loading conditions

In this paper, an efficient and effective crystal plasticity model is proposed for porous HCP crystals subject to a variety of multiaxial loading conditions. These conditions include (i) uniaxial, biaxial, and triaxial, (ii) tension and compression, (iii) low and high triaxiality, and (iv) axisymmetric and non-axisymmetric loadings. The framework is based on a combination of variational homogenization, phenomenological extensions, and assumptions motivated by observations from the high-fidelity micromechanical analysis. A novel penalty-free algorithm is employed to reach and maintain a specified stress state while performing representative volume element (RVE)-based crystal plasticity finite element (CPFE) analysis with porosity. The RVE studies demonstrate that the initial porosity, crystallographic orientation, and stress states have a significant effect on the homogenized mechanical responses of microscopically porous RVEs. The proposed porous crystal plasticity model is developed and calibrated using a database generated from the results of micromechanical RVE analysis. The calibrated porous model is reasonably effective in predicting the response of porous crystalline RVEs.

Two-Dimensional Stress Analysis of Thick Hollow Functionally Graded Sphere Under Non-Axisymmetric Mechanical Loading

In this paper, a functionally graded thick hollow sphere is considered for the analysis of two-dimensional steady state mechanical stress in the radial and circumferential directions under mechanical loading. Modulus of elasticity is varying with continuous nonlinear variation along the radial direction and Poisson’s ratio is kept as constant. The Legendre series and Euler differential equation are used to solve Navier equations. Geometry of the sphere is assumed in spherical coordinate system. Applying mechanical boundary conditions at inner and outer radii, we have carried out the analytical solutions for stresses, strains and displacements. In the numerical example, only internal pressure is varying along circumferential direction and external pressure is kept as zero. Displacements and mechanical stresses are presented graphically and the results are discussed numerically.

Geometry and Stability of a Double-shell Dome in Four Building Phases: The Case Study of Santa Maria Alla Sanità in Naples

ABSTRACT This research work provides a stability study for a double masonry dome during its construction process and, a consideration of the possible effects that the procedure followed for building the structure has on its current mechanical behaviour. In particular, the analysis is carried out on the Baroque dome of Santa Maria alla Sanità in Naples, a relatively small dome with a span of 12 m. The main contribution of the paper consists of making a hypothesis about the different phases of construction and demonstrating that the dome was in equilibrium during these different phases. This aspect has been rarely considered when analysing historical structures. The theoretical framework assumed refers to Limit Analysis in which the masonry is modelled as composed of rigid-unilateral material. To assess the stability of the dome, the study proposes an equilibrium analysis performed both graphically and analytically, by using the graphic statics and the membrane analysis. The results obtained from the two methods are also compared, at each stage of construction. Besides the classical graphical methodology based on the slicing technique, the membrane equilibrium solution provides a wider repertoire of equilibrium states, since it allows for biaxial stress fields and is here implemented with a new method for which the surface and the stress potential are both approximated through simplicial surfaces based on the same triangulation. This more refined analysis confirms the results obtained through graphic statics giving wider geometrical safety margins and a more detailed interpretation of the non-axisymmetric loading cases

Signal-based analysis of the dynamic behaviour of the system in inertia friction welding and its impact on part contact evolution

Inertia friction welding (IFW) is a process used to create joints with high geometrical accuracy and near net shape form. To cope with the complex phenomena occurring during welding, the majority of available studies have analysed the interaction of the workpieces to be joined under simplified conditions, in which the influence of machine assembly tolerances, spindle dynamics and system compliance have been neglected. Among the dimensional properties, the headstock-tailstock concentricity is particularly important to assess the conformity of the weld, for this reason, a novel approach was developed to investigate the physical causes behind the evolution of the radial misalignment between the two workpieces, conventionally referred to as radial runout. First an inverse approach to evaluate the equivalent pressure distribution at the weld interface and the equivalent process loads was implemented starting from the experimental data of radial runout, headstock angular speed and strain extracted with a custom monitoring system during a set of steel welds. The results showed a large variability of the pressure distribution in circumferential direction and non-axisymmetric load components in particular during the conditioning and burnoff phases. Then, the equivalent process loads were used as an input for a Timoshenko beam dynamic representation of the spindle. A good agreement between the model and the experimental data was observed with an average relative error in the radial runout of 0.085. From these results, it was possible to conclude that the lack of axisymmetry in the load components has to be attributed mainly to the misalignment between two workpieces, while the irregular runout to compliance of the system to the non-ideal process loads.

СПОСОБ Б.Н. ЖЕМОЧКИНА В РАСЧЕТАХ ПЛИТ В ФОРМЕ ЧАСТИ КРУГА ИЛИ КОЛЬЦА НА ПРОИЗВОЛЬНОМ УПРУГОМ ОСНОВАНИИ

Abstract. Problems of calculating slabs on an elastic foundation in polar coordinates in the traditional formulation without taking into account the shear stresses in the contact zone are considered. The shape of the plates is taken in the form of a sector of a circle with an arbitrary angle or part of a ring. Analytical solutions for such problems are known for slabs of a circular or annular plan. The calculation is carried out by the Zhemochkin method, therefore, the deflections of the slab are first determined in the form of a sector of a circle with an arbitrary angle or a part of a ring with a clamped normal. This stage of the calculation is performed by the Ritz method, where the terms of the series by the product of the powers of the radius by the trigonometric functions of the angular coordinate are taken as the coordinate functions. The expressions obtained for the deflections of a slab with a clamped normal make it possible to form a system of resolving equations of the Zhemochkin method, the solution of which is the linear and angular displacements of the introduced clamping and the distribution of reactive stresses under the slab. Further, by known methods, the movements of the slab on the elastic foundation and the forces in it are determined. Two examples are given for slabs in the form of a semicircle and an annular sector with a right angle on an elastic half-space. The results obtained can find application in the calculation of circular and ring foundations for non-axisymmetric loads and slab foundations of complex shapes in polar coordinates.

Analytical Elastoplastic Solutions for Deep-buried Circular Tunnels Under Asymmetric Load

The elastoplastic analysis of the surrounding rock of a circular tunnel is a very classic rock and soil mechanics problem. Previous scholars usually studied the situation under axisymmetric load, and they usually did not take the non-axisymmetric load distribution under the influence of ground stress and lateral pressure into account, which greatly affected its application in engineering practice. Approximate analytical solutions for calculating the plastic zone range, stress field and displacement field of the surrounding rock of a circular tunnel are inseparable from the consideration of the strength reduction and volumetric dilatancy characteristics of the rock material. The elastic-softening-residual plastic triple linear stress-strain model and the Mohr-Coulumb failure criterion are involved. The approximate analytical solutions of the residual stress field, strain field, displacement field and radius of the plastic zone in the elastic zone, plastic softening zone and surrounding plastic zone of the circular tunnel surrounding rock under axisymmetric load are deduced. The analytical solutions are valid only when the plastic zone is large and the lateral pressure coefficients 1≤λ<3. The approximate analytical method is close to the calculation result of finite element method and can replace the finite element method to carry out simple elastic-plastic analysis of surrounding rock.

К РАСЧЁТУ ЭЛЛИПТИЧЕСКОГО ЛОМАТЕЛЯ С ЭФФЕКТОМ ПАМЯТИ ФОРМЫ

The investigation purpose consists in the development of a calculation model of a thermo-mechanical power device intended for destruction of concrete structures and hard mineral rock. Its operation principle is based on the transformation of the initial round cross-section into the oval one during realization of alloy form memory that ensures a wedging effect. &#x0D; There is offered the solution of the problem on linear effort definition of a crusher at its impact upon well sides depending on rock resistance and capacity of thermo-mechanical return. The investigation method consists in the modeling of a power pipe with the cylindrical shell at its non-axisymmetric loading as a deformation-power analogue of which a thermo-mechanical diagram is accepted. The essential condition of such an approach is the identity of a task and deformation restoration with samples at the diagram formation and a power element in the structure. &#x0D; Thereupon fundamentally new is a calculation definition of the parameters of reactive stress dependence upon the deformation value of under-restoration at radial bending according to the diagram at the specified deformation by stretching that allows excluding a labor-intensive experiment. &#x0D; As a result of the investigations there are obtained formulae for the definition of a linear effort and also for the computation of pipe dimensions within the limits of design calculation. &#x0D; There is shown an actual example of power characteristics definition. The calculation reliability is confirmed with the application of these power devices during radioactive concrete structure destruction at one of nuclear power plants and at hard rock destruction at emerald field development. In such a way, the thermo-mechanical crusher design offered and a corresponding procedure for calculations can be used in practice without any changes.

Seismic Analysis of Open-Top Storage Tanks With Flexible Foundation

The behavior of aboveground storage tanks subjected to seismic excitation was investigated using numerical methods by taking flexibility of foundation into account. The hydrostatic load due to stored liquid has an axisymmetric distribution on the tank shell and base. However, during seismic events, the hydrodynamic load originating from the seismic acceleration of liquid in the tank starts to act in the direction of the earthquake motion. This leads to a nonaxisymmetric loading distribution, which may result in buckling and uplifting of the tank structure. Finite element models were created having nonlinear material properties and large deformation capabilities. Three different tank geometries with liquid height to tank radius aspect ratios of 0.67, 1.0, and 3.0 were selected representing broad, nominal, and slender tanks. These tanks were subjected to two different hydrodynamic loading based on Housner's and Jacobsen–Veletsos' pressure distributions, which forms the basis of design provisions used in American Petroleum Institute API 650 and Eurocode 8, respectively. These pressure distributions were formulated under the assumption of rigid tank wall and base. Furthermore, each tank for a given geometry was subjected to two different foundations: (1) representing a rigid foundation and (2) representing a flexible foundation. The flexible foundation was created using a series of compression-only elastic springs attached to tank base having equivalent soil stiffness. Static analysis corresponding to maximum dynamic force was performed. The finite element results for circumferential and longitudinal stress in the shell were compared with the provisions of API 650. It was found that the effect of foundation flexibility from the practical design point of view may be neglected for broad tanks, but should be considered for nominal and slender tanks.

Stress-strain state of the pipe-tank system under tank bottom settlement

The article presents a numerical model of a tank with a pipe header unit developed by the authors. The numerical model was developed considering the real geometric shape and size of the object. The model also considers the non-linear properties of the steel from which the tank and pipelines are made. This article solved the contact problem of connecting the pipeline with the wall, considering the fixed joint based on the “bonded” contact. The peculiarities of the contact interaction of pipe header pipelines with sliding supports are considered. The authors developed a design scheme for deformations of the structure under settlement. Thus, according to the results of the calculations, new dependences of the maximum effective equivalent stresses in the metal in the area of pipe header pipelines connection with the wall on the settlement value were obtained. The results obtained reflect the real stress-strain state of the metal structures of the tank under non-axisymmetric loading. The dependences obtained allow us to determine the areas of occurrence of limiting states, in accordance with which an operational decision is made about the need for repair or the possibility of continuing the tank operation, which confirms the practical significance of this study.

Analysis of the economic efficiency of major repairs of the tank foundation by the displacement method

The article features the application of a method of displacement during major repairs of vertical steel tank bases. Premises on the effectiveness of the application of the displacement method for repairing the bases of vertical steel tanks in comparison with the traditional method of repair are put forward. The comparative characteristics of the displacement method and the traditional method of major repairs of the bases of vertical steel tanks are given. The authors proposed a method of temporary displacement of vertical steel tanks, which is new for Russian practice of major repairs. An algorithm for calculating the cost-effectiveness of repairing the bases of VSTs is developed both by the traditional method and by the displacement method proposed by the authors. Technical solutions are substantiated considering calculating the stress-strain state of tank structures under nonaxisymmetric loading. A model is formed and basic parameters of the economic efficiency evaluation of major repairs of the vertical steel tank base are determined. Evaluation of the economic efficiency of major repair procedures and further maintenance of the repaired tank bases is carried out. A high economic efficiency of the new technological method of displacement is proved in comparison with the traditional method.

Analytical expression of mechanical fields for Gurson type porous models

In this work, analytical expressions of mechanical fields are provided for strain hardening thermo-viscoplastic porous materials containing spheroidal voids subjected to homogeneous strain rate loading. Explicit relationships are provided for the macroscopic stress, the plastic multiplier, the effective equivalent plastic strain rate in the matrix when the constitutive behavior of the porous medium is of Gurson type model. Axisymmetric and non-axisymmetric loadings are considered. The behavior of the porous material is governed by the model developed by Gologanu et al. (Gologanu, M., Leblond, J.-B., Perrin, G., Devaux, J., 1997, CISM Courses and lectures,377, 61–130). The particular case of the Gurson model (Gurson, A. L., 1977, ASME Journal of Engineering Materials and Technology 99, 2–15) is also investigated since it is widely adopted in the literature for analytical modeling or finite elements calculations. Various matrix behaviors are considered. The matrix is first considered as rigid perfectly plastic. Interestingly, the approach is also valid for nonlinear viscoplastic material with work hardening and temperature dependency. Extensions are also considered when the matrix material is orthotropic. Finally, the numerical implementation is discussed and it is shown that by adopting the proposed approach, the efficiency of the radial return algorithm can be improved.

3D finite element formulation for mechanical–electrophysiological coupling in axonopathy

Traumatic injuries to the central nervous system (brain and spinal cord) have recently been put under the spotlight because of their devastating socio-economical cost. At the cellular scale, recent research efforts have focussed on primary injuries by making use of models aimed at simulating mechanical deformation induced axonal electrophysiological deficits. The overwhelming majority of these models only consider axonal stretching as a loading mode, while other modes of deformation such as crushing or mixed modes – highly relevant in spinal cord injury – are left unmodelled. To this end, we propose here a novel 3D finite element framework coupling mechanics and electrophysiology by considering the electrophysiological Hodgkin–Huxley and Cable Theory models as surface boundary conditions introduced directly in the weak form, hence eliminating the need to geometrically account for the membrane in its electrophysiological contribution. After validation against numerical and experimental results, the approach is leveraged to model an idealised axonal dislocation injury. The results show that the sole consideration of induced longitudinal stretch following transverse loading of a node of Ranvier is not necessarily enough to capture the extent of axonal electrophysiological deficit and that the non-axisymmetric loading of the node participates to a larger extent to the subsequent damage. On the contrary, a similar transverse loading of internodal regions was not shown to significantly worsen with the additional consideration of the non-axisymmetric loading mode.

Thermostressed State of Layered Bodies of Revolution Damaging Under Deformation

A technique of describing the damage of deformable inelastic isotropic and elastic orthotropic materials in studying the thermoelastoplastic stress–strain state of compound bodies of revolution under nonaxisymmetrical loading and heating is proposed. The numerical results are plotted and analyzed.

Creep analysis of the FG cylinders: Time-dependent non-axisymmetric behavior

In this paper history of stresses, strains, radial and circumferential displacements of a functionally graded thick-walled hollow cylinder due to creep phenomenon is investigated. The cylinder is subjected to an arbitrary non-axisymmetric two dimensional thermo-mechanical loading and uniform magnetic field along axial direction. Using equilibrium, strain-displacements and stress-strain relations, the governing differential equations of the problem containing creep strains are derived in terms of radial and circumferential displacements. Since the displacements are varying with time due to creep phenomenon, an analytical solution is not available for these equations. Thus, a semi-analytical procedure based on separation of variables and Fourier series together with a numerical procedure is employed. The numerical results indicate that the non-axisymmetric loading and the material grading index have significant effect on stress redistributions. Moreover, by proper selection of material for any combination of non-axisymmetric loading, one can arrive suitable response for the cylinder to achieve optimal design. With some simplifications, the results are validated with the existing literature.

Determination of the region of the limiting states occurrence in RVS-20000 with the subsidence of the external bottom contour

The problem of the limiting states occurrence in the structures of a vertical steel tank is investigated in this work. To study the SSS of the metal structures of the object, the authors created a numerical model of the RVS-20000 tank in the ANSYS software complex. The model considers the maximum number of elements with their geometry and connections affecting the tank SSS under non-axisymmetric loading, including beyond the elasticity of steel. Dependences between the parameters of intrinsic stiffness of the VST are obtained. The results of the finite element analysis made it possible to develop a technique for assessing the technical condition of the structure with the development of irregular subsidence of the external bottom contour. The proposed technique can be used by both operating and design organizations in making managerial decisions regarding the repair of RVS-20000 subjected to the base subsidence.

Effect of artery pulse on the osteonal interstitial fluid flow behavior

There are two main types of fluid in bone tissue: blood and interstitial fluid. The metabolism of cells mainly relies on the microenvironment of the interstitial fluid. Researches of osteonal fluid seepage behavior based on the microstructure of bone tissue have become a hot point. The aim of the present research work is to assess the effect of blood pressure oscillation on the osteonal interstitial fluid seepage behavior. We established finite element osteon models for a hollow and that considering blood pressure oscillation, respectively, with COMSOL Multiphysics software in order to compare their fluid flow behavior under the axial loading. The results predicted that the interstitial fluid pressure field was enlarged considering the blood pressure oscillation, while the velocity filed changed little. Specifically, the increase of blood pressure oscillatory amplitude could result in the increase of osteonal interstitial fluid pressure, while the blood pressure oscillatory frequency had limited effects on the osteonal pore fluid pressure. Moreover, the blood pressure oscillatory amplitude and frequency had no effect on the osteonal interstitial fluid velocity. The finite element model can be used for the study of the poroelastic behaviors of the osteon under non-axisymmetric loads and microcracks, and can also be a new way to study the mechanism of bone mechanotransduction and electromechanotransduction.

Axisymmetric structural optimization design and void control for selective laser melting

Additive manufacturing processes, of which Selective Laser Melting (SLM) is one, provide an increased design freedom and the ability to build structures directly from CAD models. There is a growing interest in using optimization methods to design structures in place of manual designs. Three design optimization problems were addressed in this paper. The first related to axisymmetric structures and the other two addressing important design constraints when manufacturing using SLM. These solutions were developed and applied to a case study of a turbine containment ring. Firstly, many structural components such as a turbine containment ring are axisymmetric while they are subjected to a non-axisymmetric load. A solution was presented in this paper to generate optimized axisymmetric designs for a problem in which the mechanical model was not axisymmetric. The solution also worked equally well for generating a prismatic geometry with a uniform cross section, requiring no change in the procedure from axisymmetric designs to achieve this. Secondly, the SLM process experiences difficulties manufacturing structures with internal voids larger than a certain upper limit. A method was developed that allowed the designer to provide a value for this upper limit to the optimization method which would prevent the generation of internal voids larger than this value in any optimized design. The method calculated the sizes of all the voids and did not increase their size once they reached this limit. It was also aware of voids near each other, providing a minimum distance between them. Finally, in order to remove the metal powder, that fills the internal voids of structures built using SLM to reduce unnecessary weight, a method was developed to build paths to join the internal voids created during the optimization process. It allowed the analyst to nominate suitable path entrance locations from which powder could be removed, then found the shortest path connecting all voids and these locations. For axisymmetric structures it also distributed this path around the circumference to avoid generating weak points.

Gradient-enriched finite element methodology for axisymmetric problems

Due to the axisymmetric nature of many engineering problems, bi-dimensional axisymmetric finite elements play an important role in the numerical analysis of structures, as well as advanced technology micro/nano-components and devices (nano-tubes, nano-wires, micro-/nano-pillars, micro-electrodes). In this paper, a straightforward mathcal {C}^{0}-continuous gradient-enriched finite element methodology is proposed for the solution of axisymmetric geometries, including both axisymmetric and non-axisymmetric loads. Considerations about the best integration rules and an exhaustive convergence study are also provided along with guidances on optimal element size. Moreover, by applying the present methodology to cylindrical bars characterised by a circumferential sharp crack, the ability of the present methodology to remove singularities from the stress field has been shown under axial, bending, and torsional loading conditions. Some preliminary results, obtained by applying the proposed methodology to notched cylindrical bars, are also presented, highlighting the accuracy of the methodology in the static and fatigue assessment of notched components, for both brittle and ductile materials. Finally, the proposed methodology has been applied to model the unit cell of the anode of Li-ion batteries showing the ability of the methodology to account for size effects.