Tensegrity system dynamics based on finite element method

Modern fiber composites have extremely high specific strength and stiffness, significantly exceeding the corresponding characteristics of traditional metal structural materials. In the present work, the effect of the elastic modulus of circular and spiral ribs on the stress-strain state of a composite mesh compartment with cutouts reinforced with bezels investigated. For the calculations, the finite element method is used, which makes it possible to naturally consider the cutouts, stepwise varying thicknesses, various kinds of boundary conditions, and loads. The computational model of the composite lattice structure consisting of ribs is a finite element model constructed from beam elements. The parameters of the stress-strain state of a composite mesh compartment with notches reinforced by edgings are determined. The graphical dependences of the values of maximum stresses in the ribs and sheathing on the value of the modulus of elasticity are presented for the first time. The analysis of the obtained results carried out, which makes it possible to develop recommendations for an informed choice of carbon fabric types with different physical and mechanical characteristics for manufacturing the spiral and ring ribs, as well as the skin of the designed composite mesh compartments.

Eulerian-Lagrangian localized adjoint methods for a nonlinear advection-diffusion equation

Stability analysis of single-phase thermosyphon loops by finite-difference numerical methods

Numerical analysis and physical consideration of vocal fold vibration by modal analysis

Strip profile and shape control affects strip geometric quality mill productivity, and customer’s satisfaction. Since strip shape control is conducted by altering strip profile, the accuracy of predicted strip profile plays the most important role in the real-time crown and shape control. A simple and efficient model is required to accommodate various material grades, widths, gauges, rolls, crown control devices, and operating conditions. This article proposes a simplified numerical method to predict strip profile. The mill is simulated by the beams (rolls) on the infinite elastic half space (between rolls and strip). The roll deflection and indentation are calculated using the influence coefficients and Boussinesq’s equations respectively. The roll contours in the contact zone can be expressed in terms of the influence coefficient and indentation matrices. The no-load gaps between rolls and strip are assumed to be closed completely under the rolling pressure. The compatibility equations are derived by matching two surface profiles in the contact zone. The roll crowns considered in the compatibility equations include the ground crown, the thermal profile, and the roll wear. The equilibrium equations ensure the force and moment balance of the strip and each roll. A complete full-rank linear system is then established by assembling the compatibility and equilibrium equations of all rolls and strip. Solving the linear system leads to the contact rolling pressure distribution and the rigid motion of the roll chocks. The roll surface contours and strip profiles can be further calculated accordingly.

The equilibrium dual discrete mathematical models of the problems of limit load analysis and optimization are investigated in the article. These models are presented in terms of static and kinematic formulation using equilibrium finite elements. In these mathematical models the possible discontinuities of displacement velocities are evaluated and the velocity of energy dissipation is estimated not only within the volume of finite elements, but at the plastic surfaces between elements. At first, on the basis of the energy principle of the maximum external power [1,2] the general mathematical models (3) and (7) of static formulation of limit load analysis and optimization problems are created. In these models the yield conditions are controlled not only within the volume, but also at the surfaces of finite elements. The equilibrium finite elements and interpolation functions of strains (9) are used for discretization of these models. The constancy of external power is taken as the optimum criterion. The discrete expressions of fundamental relationships—equilibrium and geometric equations, yield conditions (10)-(12) for finite element and (14)-(17) for the discrete model of a body are developed. The discrete expressions of yield conditions are given using the classic collocation methods: collocation at the point, collocation at the sphere (element) and Bubnov-Galiorkin's collocation method [11,12]. The equilibrium equations of discrete structure are developed on the basis of virtual displacement principle while geometrical equations are derived using virtual force principle. In contrast to the approach of other authors, yield conditions and geometrical equations are described not only within finite elements, but also at the surfaces between elements. That helps to design the dual discrete mathematical models of the problems (21)-(26), in which the discontinuities of displacement velocities and the velocity of energy dissipation in the place of those discontinuities are estimated. The mathematical models (22), (24), (26), (29) and (32) of kinematic problem formulation are developed from sensible static formulations by Lagrange's multiplier method. The modified mathematical models (27)-(29) are presented. In these models the equilibrium equations are eliminated or the geometrical equations are transformed into compatible equations of plastic stress velocities, in this way decreasing the number of equations and unknown values. The dependence of the numerical results (limit load) of the frame on the approximation degree of bending moments, as well as on the discretization method of yield conditions are illustrated. In table 1 the values of limit loading parameter F 0 and their error of calculation ΔF 0 (per cent, in comparison with the analytic solution F 0 = 0,4662M 0) are presented. They are given for the first and second order finite elements with linear and parabolic distribution of bending moments using different discrete yield conditions and a different number of finite elements. The numerical result shows, that the discretization of yield conditions by Bubnov-Galiorkin's method gives the best accuracy and stable solutions. By discretizing yield conditions using the point's collocation and collocation at the element, the accurancy of numerical results depends not only on the number of elements, but also on a more or less successful choice of finite elements net.

In engineering domains, modal analysis is a field that is studied extensively with the goal of better characterizingcomponents or structures. Themodal analysis produces modal parameters, which are essential properties of a system that can be employed for damage identification, vibration analysis, and structural health monitoring. Plated element’s relevance in variousapplications makes it an intriguing vibration study subject. In thisresearch, modal analysis was performed on a square steel plate in free ends condition. This work aimedto provide a complete anatomical description of this complex boundary condition and its implications on modal parameters. Before comparing modal parameters with experimental data, a primary modal analysis was performed using finite element (FE)method. Then experimental analysis was conducted under the operational modal analysis setup (OMA).As the results, six natural frequencies are retrieved and compared amongst the two methods, recording the maximum of 6% percentage difference from the readings. This implied a close values estimated between the methods used. For mode shapes, ninemodes are identified from FE method and discussed according to established free plate vibration studies, while threesimilarly identified modes successfully recognized by using OMA.

The vibrations developed during the work represent one of the main mechanical problems of the electric motors. Their frequencies and levels can cause large damages of different electrical motors parts. This is the reason why even in the design phase it is useful to be known the values of the natural frequencies of the parts. This can be made in two different ways: using modern capabilities of finite element method (FEM) or doing experimental modal analysis. The study developed in the present paper refers to the modal analysis of a three-phase squirrel cage induction of 1.5 kW, for both, for its elements and, for motor and the electric motor as an assembly. The FEM modal analysis was applied using ABAQUS software for assembly of the 7 elements of the motor. The 3D model was developed, mechanical connections being of screw type. The theoretical model was validated by experiments, with impact hammer test method. The validation confirms the assumptions made for the 3D model and the designed model can be use, as example, for other FEM based modal analysis. The natural frequencies obtained both by FEM and experimental method does not overlap on the working frequencies.

Abstract: The problem of plane elasticity for a doubly connected body with inner and outer boundaries in a regular polygonal form with common centre and parallel sides has been studied. The sides of the polygon were exposed to external forces. The nature of the force term was determined by application of complex variable theory. Kolosov’s method of solution was applied to obtain the biharmonic equation of the forcing term. The forces on the particle were studied under 2-dimensions from which the compatibility and equilibrium equations were derived. The compatibility and equilibrium equations were used to derive the force – stress relations. The results shows that there is a significant relationship between the angle of the force term on the plane of the particle and the stress state of the particle, which is in conformity with existing experimental results.

The presented work discusses the vibration behavior of an axial turbine, analyzed using the finite element method (FEM) using commercial software ANSYS®. The turbine was modeled as a 2-D plate type of structure discretized with 4-noded shell 63 elements to save computational time. Constraints were applied keeping in view the actual operating conditions. The turbine was modeled with more than one FE meshes. Mesh sensitivity analysis was carried out to ensure the quality and independence of the results. Modal analysis was conducted to calculate a few initial natural frequencies. Results were studied against the operating frequency of the turbine. After carrying out the modal analysis, harmonic analysis was performed to see the response of the turbine under dynamic loading. The nature and cause of the dynamic loading are also discussed in relation to dynamic behavior. It was observed that the turbine is safe in its entire range of operation as far as the phenomenon of resonance is concerned. Also, it was observed that the maximum harmonic response of the turbine on the application of dynamic loading is far lesser than its failure limit within the specified operating range.

Connecting rod is one of the major components in the automotive engine which transmits the reciprocating motion of the piston into the rotary motion of the crankshaft. The engine’s performance and efficiency are greatly influenced by the optimum design of the connecting rod. This numerical investigation ascertains the effect of shape and mass on the transient structural stability and integrity of the connecting rod. The solid model of the connecting rod is developed using PTC Creo. The kinematic movements between the joints and forces are assessed using the rigid body dynamics approach. The shape and mass of the connecting rod are optimized by using the shape finder tool of the finite element method using the outcomes of rigid body dynamics. The optimized connecting rod possesses better structural stability and comparable factor of safety as evaluated by comparing the transient structural deformation, localized and equivalent von-misses stress of the standard and shape optimized connecting rod.

When a simplex finite element method is applied to solve a linear differential equation governing a region enclosed by curved boundaries, the boundaries are obliged to be represented by a polyline. Boundary conditions of the second kind are specified as the derivatives normal to the boundaries, causing numerical error in the results. This paper concerns a finite element method using linear-triangular elements, in which boundary conditions of the second kind are introduced more accurately. When the curved boundaries move or rotate, the resultant error is remarkably improved, and the number of nodes can be decreased.

In this master's thesis work, finite element method limitations are investigated in the dynamic analysis of reinforced panels. The panel was modelled using different meshes in order to show that, depending on the element length (or the number of degree of freedom) used in the model, the model does not properly stand for the real structure. In order to assess experimentally the model, an aluminum reinforced panel was built and, through experimental methods, a modal analysis was carried out. The finite element modelling limits were tested and compared to experimental results regarding mid-frequencies. A comparison between finite element and spectral element methods was carried out for computational cost reduction purposes. Due to uncertainties of some model input parameters, a statistical variation was performed using Monte Carlo and Surface Response methods. Results have shown that, at high frequencies the finite element method is not appropriete for dynamic analysis due to high computational costs in high frequency and it is highly sensitive to small variations of the input parameters.

In this work, derivation of equations of a mixed type for shallow shell constructions of an arbitrary type is carried out by means of the variational method. Such equations are more simplified equations of the shell theory, as compared to equations in displacements, but in case of some types of fixing of shell edges (for example, in case of pin-edge and movable fixing) they are more convenient. The mathematical model of shell deformation is based on the Kirchhoff–Love hypotheses, geometrical nonlinearity is taken into consideration. The full functional of shell energy is used for derivation of equilibrium equations and the third equation of strain compatibility in the middle surface of a shell, its minimum condition (the first variation of the functional has to be equal to zero) giving place to these equations. The stress function is entered in the middle surface of the shell in such a way as to make the first two equilibrium equations vanish identically. Thus, the third equilibrium equation and the equation of strain compatibility give the equation of a mixed type in relation to the deflection function and the stress function in the middle surface.

Constitutive laws for elastic-plastic materials are derived by eliminating the transverse stress component on the basis of the plane-strain constraint. This leads to a fictitious hardening and temperature dependence of the loading function. For standard elastic-plastic materials the resulting laws are associated; however, the plastic strain state is represented by equivalent plastic-strain measures, which also account for transverse yielding. The new constitutive laws, together with the standard reduced form of the equilibrium and compatibility equations, permit the formulation of the plane-strain elastic-plastic analysis problem in terms of the in-plane stress components only. In the case of perfectly plastic materials, the subsequent plane-strain yield surfaces are contained within a domain bounded by a limit surface which represents the yield condition normally adopted in plane-strain limit analysis.