Physical Nonlinearity Research Articles

Automation of assessment of the strain state of metal cutting machine mechanism elements on the basis of response function application

The article dwells upon the assessment of the strain state of metal-cutting machines with the help of the numerical method of finite elements in the form of displacements. A metal-cutting machine is considered as a system consisting of a set of structural elements taking a set position in space in relation to each other, and a part of them may execute relative motions (displacements). The paper suggests a modification of the finite element method on the basis of combining a set of finite elements into a group with the use of the response function. The author provides an analytical calculation method to resolve the problem of assessing the strain state of the machine mechanism elements in linear and non-linear settings. The developed algorithm allows analyzing geometrical, physical and contact non-linearity of metal working. The research provides a practical implementation of the developed method by the examples of assessing the strain state of a rod element modeling the roughness of the contact surface of the machine mechanism elements under temperature and tensile loads.

ОПРЕДЕЛЕНИЕ ПРОЧНОСТИ ГРУЗОВОГО ПОЛУВАГОНА ИЗ АЛЮМИНИЕВЫХ СПЛАВОВ С УЧЕТОМ ФИЗИЧЕСКОЙ НЕЛИНЕЙНОСТИ ОТ РАСПОРА СЫПУЧИМ ГРУЗОМ

ОПРЕДЕЛЕНИЕ ПРОЧНОСТИ ГРУЗОВОГО ПОЛУВАГОНА ИЗ АЛЮМИНИЕВЫХ СПЛАВОВ С УЧЕТОМ ФИЗИЧЕСКОЙ НЕЛИНЕЙНОСТИ ОТ РАСПОРА СЫПУЧИМ ГРУЗОМ

Failure analysis of laminated composites with shear nonlinearity and strain-rate response

Prediction of the mechanical response and failure behavior of laminated composites is vital for an efficient design in engineering applications. Vast quantity of failure models for composites were developed and compared in accuracy and applicability. In practice, many concerns usually appear at the material and damage model selection stage, since some models are not sensitive to important mechanical effects, while others are too complicated and require a large amount of experimental data. Presented work proposes a flexible approach for a failure modelling and initially requires only minimum of commonly available experimental data, but with possibility of extension to capture different forms of physical nonlinearity, including nonlinear shear and strain-rate effect. Proposed failure model is based on introduction of two damage parameters. Nonlinear shear response is formulated by introduction of an arbitrary polynomial shear stiffness dependency on shear strain component. Strain rate effects are considered using damage rate parameter, which has some advantages in constitutive equation formulation and practical usage. Special analytical relations for damage rate influence are presented with successful test correlation. Proposed model was implemented in commercial finite element analysis software via special user subroutines for practical computations. Numerical simulations for example problems of composites under biaxial loading and open-hole compression plate test were performed and a good correlation between theoretical and experimental results were achieved.

The effect of cracks on the bearing capacity of reinforced concrete slabs

Cracks occur in reinforced concrete slabs for two reasons - due to increased operational loads and due to manufacturing and installation defects. When cracks are detected, the question arises about the residual bearing capacity of the slab and the need of its strengthening. To solve this problem by calculation, it is necessary to take into account physical nonlinearity. An algorithm for the calculation by the finite element method is proposed. The main feature of the algorithm is the use of multilayered finite elements, which allows modeling the cracks by specifying the corresponding material characteristics of those layers which the crack passes through. A method for determining the bearing capacity of a slab with cracks after its reinforcement with composite fabrics is also considered. An example of the study of the stress-strain state of a reinforced concrete slab with cracks by the proposed method is given. The implementation of the algorithm in the PRINS program is described and the possibility of using this program for solving practical problems is discussed.

Computer modeling of the wind power unit constructions with power over 2 MW

The aim of this work is to evaluate the efficiency of the system “steel tower reinforced concrete foundation – foundation ground” of a wind power unit with power more than 2 MW using computer simulation in ANSYS. For this purpose, an example of a wind power unit is taken from the previous work, but in this case the lower part of the tower up to height of 20 m was filled with B60 concrete. The second distinctive feature of the presented wind power unit is the use of a collapsible foundation, which was manufactured according to our patent. The simulation takes into account the spatial reaction of elements of the structural system and the physical nonlinearity of the materials from which they are made. In this case, for steel the von Mises theory of strength was used, for concrete the Williams-Varnack theory was used, and for ground base the Drucker-Prager theory was used. Comparison of the obtained results with data of previous work showed that the breaking load of tower has increased by 57% due to filling the lower part of the tower by concrete, which indicates the efficiency of the proposed solutions.

Estimate of dynamic load capacity of reinforced concrete deep beam made of very high strength construction materials

The paper presents an analysis of the dynamic load capacity of a dynamically loaded rectangular reinforced-concrete deep beam made of high-strength materials, including the physical nonlinearity of the construction materials: concrete and reinforcing steel. The solution was acquired with the use of the method presented in [15]. The dynamic load capacity of the reinforced concrete beam was determined. The results of numerical solutions are presented, with particular emphasis on the impact of the very high strength of concrete and steel on the reinforced concrete beam’s dynamic load capacity. The work confirmed the correctness of the assumptions and deformation models of concrete and steel as well as the effectiveness of the methods of analysis proposed in the paper [1, 15] for the problems of numerical simulation of the behaviour of reinforced concrete deep beams under dynamic loads. Keywords: mechanics of structures, reinforced concrete structures, deep beams, dynamic load, physical nonlinearity.

Analysis of oscillations of framework at pulse influence taking into account physical non-linearity

Analysis of oscillations of framework at pulse influence taking into account physical non-linearity

Sztywności przekrojów żelbetowych i analiza belek z uwzględnieniem nieliniowości fizycznych

Sztywności przekrojów żelbetowych i analiza belek z uwzględnieniem nieliniowości fizycznych

Design Analysis of a Typical Steel Frame of a High-Rise Industrial Building After an Accident

The article considers the high-rise industrial building with typical design solutions, which was severely damaged as a result of an emergency (fire).The main objective of the work is to perform a design analysis of the steel frame of the building, determine the stress-strain behaviour and assess the load-bearing capacity of the elements considered at all stages of the structural behaviour. Calculations were made taking into account the stress history, the contact between the model elements, and also taking into account geometric, physical and structural nonlinearities. The structural behaviour analysis was made with explicit and implicit schemes of forth integration of the equation of motion. The article presents a numerical solution of the problem for calculating the combined power and temperature effects for the model frame of the high-rise industrial building in accordance with the thermal behavior of “real” fire and gives assessment of stability of the initial structural layout to the progressive collapse. Based on the results of the analysis, conclusions were drawn and recommendations were given to increase the stability of load-bearing structures of such buildings to a chain, progressive collapse. The results of calculated analysis were used in the design phase of the project to strengthen the load-bearing elements, as part of support of construction and installation work to reconstruct the frame, as well as during structural monitoring.

To the approximation of rectangular and complex cross-sections of reinforced concrete structures under the action torsion with bending

Special analytical method for determining tangential tension stresses in reinforced concrete structures operating in conditions of complex resistance –torsion with bending is proposed in this paper. Its peculiarity consists in the approximation of rectangular and any complicated cross-sections of reinforced concrete structures with the help of their division into squares with the circles inscribed there in, connected together into a single monolithic figure. The dependence of tangential torsion stresses becomes valid on the distance to the centre of the circle under consideration within each j-th circle. The further the circle from the centre of the rectangle is located, the greater its moment of inertia becomes and the maximum stresses are reached in the middle of the rectangle the long sides. Such model makes it possible to remove the question of the necessity using of special tables also for their calculation in the elastic stage. Also it makes possible to separate the stress-strain state in a whole set of circular sections from the additional field associated with the deformation of the rectangular section. The authors corrected and significantly supplemented the dependencies for taking into account the deplanation of a rectangular cross-section rod. Attention is focused on the physical essence of longitudinal displacements caused by deplanation, an analogy with elementary movements caused by shearing forces is carried out. In the study, the classification of spatial cracks for reinforced concrete rod structures under the action torsion with bending was generalized; while the process of spatial cracks formation of the first, second, and third types is tied to the proposed method for determining tangential stresses (angular deformations) for complex cross-sections. The proposed dependencies allow us to search for the values of the model design parameters at of the stress-strain state stages of the reinforced concrete rod structure, including in the plastic and in the limiting stages. The components of the torsion stress (angular deformations) are again synthesized and separated by the proposed method for the convenience of analysis in principal stresses tensors (main strains). Transformational transitions from a cylindrical to a Cartesian coordinate system and the attraction of local coordinate systems made it possible to simplify the equations as much as possible. Moreover, the equations are constructed in such a way that the resolving system does not turn into a decaying system. The physical interpretation of the solution obtained, with respect to the problem of crack resistance, is that it allows us to search for the minimum generalized load that corresponds to the formation of the first, second or third spatial crack types and the coordinates of their formation point. As a result, the effectiveness of the proposed method is shown with approximating rectangular and complex cross sections of reinforced concrete structures under the action torsion with bending and taking into account physical nonlinearity, deplanation of cross-sections, pre stressing in longitudinal and transverse reinforcement and the influence of local stress fields.

Modelling of Contact Interaction with Allowance for Nonlinear Compliance in Unilateral Constraints

The finite element model and numerical solution of the contact problem in the presence of nonlinear deformable layer between interacting bodies are considered. To discretize the contact layer, frame-rod contact finite elements are used, which also model different contact states (separation, clutch, friction-slip, etc.). The use of frame-rod contact elements allows the physical nonlinearity of the contact layer to be reduced to the internal nonlinearity of the system of contact elements, while the nonlinear properties of the seam will be set through the nonlinear characteristics of the individual rods of the contact elements. The numerical algorithm for solving the contact problem is based on the method of step-by-step analysis with iterative refinement of the solution for the current load level. With its help, the numerical solutions of the problem of contact of the structure with the base under different conditions of the contact seam have been obtained and analyzed.

Introducing Physical Nonlinearity in the Design of Aluminum-Alloy Vehicle Components

The application of the finite-element method in the design of vehicle components consisting of physically nonlinear materials is possible by parabolic approximation of the actual deformation diagram. Taking account of physical nonlinearity permits satisfactory design of the load-bearing structures in vehicles.

Contact interaction of machine elements with non–linear elastic intermediate layer

The work presents a variational formulation of a contact problem for elastic bodies with an intermediate nonlinear contact layer. The layer is introduced in order to model compliant gaskets, coatings and roughness between or on the surface of the machine parts. The contact conditions in this case incorporate not only the elastic displacements but the local deformations attributed to the contact layer. This additional deformation is determined at every point of the contact surface as a function of the acting normal tractions. This relation is in general nonlinear and can be accounted for by a special term in the complementary energy updating the original Kalker’s variational principle. As an outcome the problem acquires besides the structural nonlinearity (i.e. contact) as well the physical nonlinearity. This means that one needs to solve a system comprising both the inequalities and nonlinear equations. This is done by computing consecutive approximations from problem linearizations. The two particular variants of this procedure comprise the method of augmented gap and the method of variable compliance. Newton-Raphson iterations are also considered as an option. With this model and the numerical analysis method at hand one can solve certain inverse problems. The goal is to justify the the geometrical shape of the contacting bodies as well as the physical parameters of the contact layers. The objective criteria enforcing strength and durability in terms of the contact loads are proposed for the optimization. Furthermore deformation components arising from the applied external loads and the corresponding correction of the contact geometry are introduced as an additional design factor.

Analysis of oscillations of framework at pulse influence taking into account physical non-linearity

The article illustrates the analysis of oscillations of a flat multi-storey framework as discrete dissipative systems (DDS) at pulse influence by the time analysis method (TAM). Brief theoretical prepositions of TAM, such as description of the equation of motion of the DDS and expressions of response parameters, are given. The design dynamic model of the structure represents the flat three-storey shear frame having three degrees of freedom. The calculation results are oscillograms of internal response characteristics and reaction parameters of the system on the time slice t ϵ [0;8] sec. The multi-cycle nature of deformation of racks and also the change of parameters of plastic zones of framework supporters in the process of non-linear oscillations are considered.

Experimental and theoretical studies of biaxially prestressed steel-fiber-concrete slabs.

The article presents the results of experimental and theoretical studies of strength and deformability of steel-fiber concrete double-sided pre-stress slabs under the action of transverse loading. The simulation of such plates in the software complex LIRA-SAPR was performed taking into account the physical nonlinearity of materials.

THE COMPARATIVE ANALYSIS OF THE RESULTS OF REAL AND NUMERICAL EXPERIMENTS FOR DEFINING THE ULTIMATE BEARING CAPACITY OF LIGHT GAUGE STEEL STUDS “ATLANT”

The article in question describes the results of comparison of numerical and real experiments, presented in the report of the Canadian laboratory “Bodycote” [1]. The paper depicts the test fixture, on witch six samples (two typical sizes) of light gauge steel stud “ATLANT” were tested. As a result, dependencies between bearing capacity and characteristic displacements were received. In order to repeat the experiment, the series of computer models were created with the software ANSYS. The computer models have complex nature: geometrical / physical nonlinearity was used. For accounting steel material nonlinearity, we used a multilinear model with isotropic hardening (MISO). The proper diagram was used for each typical size in accordance with the experiments on the tensile-testing machine. For the purpose of supporting condition and load modeling which are identical to the full-scale experiment, a couple of contact elements were used. The utilization of contact elements allowed us to consider friction between the sample and the supporting structures. One of the disadvantages of the full-scale experiment is the absence of measurements of the initial geometrical imperfections. For their consideration the use of probabilistic approach is suggested. This approach entails calculation of several models with different spread of initial imperfections. The initial geometrical imperfections with stochastic nature were included in the computing model. Parameters of distribution were based on the measurements of eighty-eight C-shaped members [8]. In the result of comparison, fine precision in terms of the ultimate bearing capacity and deformation pattern were established. According to expectation, the results of the full-scale experiments were found inside the fictitious “corridor”, created in accordance with the results of computer modeling.

Analysis of steel-reinforced high-strength concrete deep beam displacement under dynamic loads

The paper presents an analysis of the deformation of a dynamically loaded rectangular reinforced-concrete deep beam, including the physical nonlinearity of construction materials: concrete and reinforcing steel. The solution was acquired with the use of the method presented in [15]. The displacement of three plate types under various loads, up to dynamic load capacity depletion, was analysed. The results of numerical solutions are presented, with particular emphasis on the impact of the very high strength of concrete and steel on the reinforced concrete plate displacement. The work confirmed the correctness of the assumptions and deformation models of concrete and steel as well as the effectiveness of the methods of analysis proposed in the paper [1, 15] for the problems of numerical simulation of the behaviour of reinforced concrete deep beams under dynamic loads. Keywords: mechanics of structures, reinforced concrete structures, deep beams, dynamic load, physical nonlinearity.

Dynamic displacement analysis of reinforced concrete deep beams made of high strength concrete. Part III: Analysis of dynamic displacement of a reinforced concrete deep beam made of high strength C300 grade concrete

This work demonstrates an analysis of the displacement state of rectangular concrete deep beams made of very high strength concrete grade C300 under a dynamic load, including the physical nonlinearity of construction materials: concrete and reinforcing steel. The analysis was conducted with the method presented in [1]. Numerical solution results are presented with particular reference to the displacement state of a rectangular concrete deep beam. The work confirmed the accuracy of the assumptions and deformation models of concrete and steel as well as the effectiveness of the methods of analysis proposed in the paper [1] for the problems of numerical simulation of the behaviour of reinforced concrete deep beams under dynamic loads. A comparative analysis was conducted on the effect of the high-strength concrete and the steel of increased strength on the displacement of a grade C300 concrete deep beam vs. the results produced in [10] for grade C100 and C200 concrete deep beams. Keywords: mechanics of structures, reinforced concrete structures, deep beams, dynamic load, physical nonlinearity.

Numerical methods for contact analysis of complex-shaped bodies with account for non-linear interface layers

In order to ensure high technical characteristics of machines for various applications, it is necessary to increase the strength of the most loaded and heavy-duty elements of constructions, which are complex-shaped components under intense contact loads. When bodies get in contact over surfaces of close shape, new factors that have not been taken into account before come into play. In particular, nonlinear contact stiffness of the surface layers of the components is among them. Accordingly, nonlinear components appear in impenetration contact conditions instead of traditional linear ones. To study the contact interaction with account for such constraints, a new method for stress-strain state analysis and structural strength design of various machine parts has been developed on the basis of a modification of the Kalker’s variational principle. Nonlinear models of the material behavior of the surface layers of contacting complex-shaped bodies were created and applied. The discretization of the resulting mathematical problem was performed with the help of the developed version of the boundary element method. The developed models of contact interaction combine physical and structural nonlinearities. This provides more accurate modelling of stress-strain state of contacting complex-shaped bodies in comparison with conventional approaches. The peculiar variation of the contact pressure distribution with the change of the gap shape and the properties of the interface layer between the contacting bodies were studied on this basis. It is possible to derive more relevant recommendations to justify design and technological solutions with account for the results of such analysis. Eventually, this will enhance the technical characteristics of machines of various applications

Investigation of the joint operation of electric transmission lines with a new type concrete reinforced concrete foundation

The aim of this work was to study the joint work of structural systems “steel bearing overhead power transmission lines 10 kV – prefabricated concrete Foundation of a new type [1] – ground”. For this purpose the technique of computer simulation in a PC “ANSYS” of the system. The method takes into account the spatial work of designs and physical nonlinearity of materials from which they are made. In addition, for steel was used in the theory of Mises, for concrete – Williams-Warnake, for ground – Drucker-Prager. In addition, all the necessary geometric, strength and physical characteristics of the model were obtained on the basis of the existing construction Standards for the design. The analysis of stress shows that its strength, stiffness and stability is provided, and there are reserves: for the metal supports – up to 15% to the base – 30%, ground – 1%.Therefore, further studies should consider the optimization problem for the choice of an effective constructive solution of the support and Foundation (with clarification on how to calculate them), that may be grounds to apply for a patent or utility model. Based on the obtained results it is recommended that a new type of collapsible foundations to apply in the real world.