Nonlinear Transient Analysis Research Articles

Geometrically nonlinear transient analysis of laminated composite super-elliptic shell structures with generalized differential quadrature method

In this study, geometrically nonlinear dynamic behavior of laminated composite super-elliptic shells is investigated using generalized differential quadrature method. Super-elliptic shell can represent cylindrical, elliptical or quasi-rectangular shell by adjusting parameters in super-ellipse formulation (also known as Lamé curve formulation). Geometric nonlinearity is taken into account using Green–Lagrange nonlinear strain–displacement relations that are derived using differential geometry and theory of surfaces. Transverse shear effect is considered through the first-order shear deformation theory. Equation of motion is obtained using virtual work principle. Spatial derivatives in equation of motion is expressed with generalized differential quadrature method and time integration is carried out using Newmark average acceleration method. Several super-elliptic shell problems under uniform distributed load are solved with the proposed method. Effects of layer orientations, boundary conditions, ovality and ellipticity on dynamic behavior are investigated. Transient responses are compared with finite element solutions.

On the Nonlinear Transient Analysis of Planar Steel Frames with Semi-Rigid Connections: From Fundamentals to Algorithms and Numerical Studies

Abstract This paper presents the fundamentals for prediction of a more realistic behavior of planar steel frames with semi-rigid connections under dynamic loading. The majority of the research in this area concentrates on the nonlinear static analysis of frames with semi-rigid connections. Indeed, few studies have contributed to the nonlinear dynamic and vibration analyses of frames. Therefore, this article first describes the frames’ semi-rigid connection behavior under monotonic and cyclic loads, and presents the independent hardening technique adopted to simulate the joint behavior under cyclic excitation. In a finite element context, this paper presents an efficient numerical methodology that is proposed in algorithmic form to obtain the nonlinear transient response of the structural system. The paper also presents, in algorithmic form, a complete description of the adopted connection hysteretic model. Satisfying the equilibrium and compatibility conditions, and assuming only the connection’s rotational deformation due to bending as variable, this work obtains the tangent stiffness and mass matrices of the beam-column element with semi-rigid connections at the ends. The study concludes by verifying and validating the proposed numerical approach using four structural steel systems: a L-frame, a two-story frame, a six-story frame, and a four-bay five-story frame. The analyses show that the hysteresis of the semi-rigid connection has a strong effect on the frames’ responses and is an important source of damping during the structural vibration.

Nonlinear Transient Analysis of Temperature Fields in an AGF Project used for a Cross-Passage Tunnel in the Suzhou Metro

This paper examines the evolution process of the freezing curtain and the transition process of unfrozen water in an Artificial Ground Freezing (AGF) project used for a cross-passage tunnel in the Suzhou Metro, China. The focus of this study was on confirmation of the rationality of the freezing design on a weak silty clay layer, using a prognosis of the temperature development by numerical simulation and field monitoring. For the above purposes, basic mathematical techniques were employed to address the nonlinear transient thermal conduction problem considering the release of latent heat. The comparison analysis of the temperatures gained by field testing versus numerical simulation was performed to verify the accuracy of the numerical model. The results indicated that the formation of a stable freezing curtain with the design thickness required more time than the estimated active freezing period. The variation of unfrozen water volumetric content within the frozen fringe is normally exhibited as a process of increase and then decline until it vanishes, whereas there was a gradual and continuous increase near the frozen fringe. Although there was a deviation in the results between field monitoring and the numerical simulation, the general temperature curves from both methods were essentially consistent.

An explicit algorithm for geometrically nonlinear transient analysis of spatial beams using a corotational total Lagrangian finite element formulation

An explicit method for nonlinear transient dynamic analysis of spatial beams with finite rotations using a corotational total Lagrangian finite element formulation is presented. The kinematics of the beam element is described in the current element coordinate system constructed in the current configuration of the beam element. The element deformation and inertia nodal forces are derived by the virtual work principle, the d'Alembert principle, and the consistent linearization of the geometrically nonlinear beam theory. A nodal rotation vector is used to represent the finite rotation of a base coordinate system rigidly attached to each node of the discretized structure. A numerical procedure of explicit method is proposed for the solution of the nonlinear equations of motion. The standard central difference method is applied to the incremental displacement vector and the incremental rotation vector, and the time derivatives of displacement vector and rotation vector. The nodal orientations are updated by the incremental nodal rotation vectors. The values of nodal rotation vectors are reset to zero in the current configuration.In order to assess the efficiency and the accuracy of the proposed method, numerical examples are studied and compared with the results obtained using the implicit method based on the Newmark method.

A New Multistep Technique Based on the Nonuniform Rational Basis Spline Curves for Nonlinear Transient Heat Transfer Analysis of Functionally Graded Truncated Cone

ABSTRACTA novel multistep method based on the nonuniform rational basis spline curves is developed for the solution of a system of nonlinear differential equations. Efficiency of the presented method in terms of convergence and accuracy is demonstrated through the two-dimensional nonlinear transient heat transfer analysis of multilayered functionally graded truncated cone subjected to an internal thermal load with radiative–convective boundary condition at outer surface. In order to discretize the governing equations in the spatial domain, a layerwise-differential quadrature method is implemented. This transforms the partial differential equations into a system of nonlinear ordinary differential equations in the temporal domain, which is then solved using the presented technique. Comparative studies between predictions of the presented multistep technique and various existing numerical methods demonstrate superior computational efficiency of the method with low computational cost. High efficiency of this method indicated that the presented multistep approach can be successfully employed in various nonlinear problems. Finally, the effects of different parameters on the transient temperature of the truncated cone are studied. It is expected that the presented multistep method will be applied on various practical engineering problems in future studies.

Nonlinear transient analysis of hole-entry journal bearing with constant flow of micropolar fluids

The present work deals with study and analysis of a symmetric hybrid journal bearing compensated with constant flow valve restrictor operating with micropolar fluid from stability point of view. The effect of micropolar parameters on the stability of this journal bearing system is presented on the basis of nonlinear transient model. Finite element method has been used to solve modified Reynolds’ equation for the flow of micropolar fluid through the bearing. Computations are done for the static and dynamic characteristics of hole-entry hybrid journal bearing system. The stability characteristics in terms of critical mass of journal, threshold speed, and frequency of whirl are obtained for journal bearing system operating with Newtonian and micropolar fluids and are compared together. Paths of the journal center in the form of trajectories have also been plotted using the journal center coordinates obtained after solving nonlinear equation of motion by fourth-order Runge–Kutta method to find the stability margin of the considered bearing configuration more precisely and easily. Results indicate that micropolar effect causes significant increase in stability margin of the hybrid journal bearing system especially at higher loads. The results also indicate that lubricant flow through the bearing and type of lubricant should be decided in an appropriate manner for the stability of the constant flow valve compensated hybrid journal bearing system.

Geometrically Nonlinear Transient Response of Laminated Plates with Flexible Supports

Laminated plates are loading-bearing components that are generally connected to flexible pads and exhibit complicated mechanical responses. To investigate the geometrically nonlinear transient responses of a laminated plate with flexible pad supports, a varied constraint reaction model and a systematic numerical procedure are presented in this paper. The flexible pad supports of the plate were treated as viscoelastic boundary conditions, wherein the strip-type pad per unit length was modeled as a cantilever beam. The nonlinear Kelvin–Voigt model was developed to simulate the nonlinear viscoelastic behaviors of the flexible pads. The dynamically varied constraint reactions generated by the viscoelastic supports, which depend upon the displacement and velocity of the nodes along the plate edge, were determined by the deflection and slope equations of the beam theory used, and they were applied on the plate edges by using the nonlinear load functions. Thus, the dynamical responses of the laminated plate with viscoelastic supports were obtained. Numerical results show that the present method can effectively treat the geometrically nonlinear transient response of the laminated plate with viscoelastic supports, and it is essential to consider the effects of non-ideal boundary conditions in the nonlinear transient analysis.

Performance analysis of smart laminated composite plate integrated with distributed AFC material undergoing geometrically nonlinear transient vibrations

The present work focuses on geometrically nonlinear transient analysis of laminated smart composite plates integrated with the patches of Active fiber composites (AFC) using Active constrained layer damping (ACLD) as the distributed actuators. The analysis has been carried out using generalised energy based finite element model. The coupled electromechanical finite element model is derived using Von Karman type nonlinear strain displacement relations and a first-order shear deformation theory (FSDT). Eight-node iso-parametric serendipity elements are used for discretization of the overall plate integrated with AFC patch material. The viscoelastic constrained layer is modelled using GHM method. The numerical results shows the improvement in the active damping characteristics of the laminated composite plates over the passive damping for suppressing the geometrically nonlinear transient vibrations of laminated composite plates with AFC as patch material.

Influence Factors Analysis of RC Beams under Falling Weight Impact Based on HJC Model

Impact loads may cause serious or even fatal damage to the structure (component), in most existing specifications in China, and there are no special terms that take impact load into consideration. So, the response analysis of the structure (component) under impact loads is very important. In this paper, the sensitivity analysis was conducted for the 22 parameters of the Holmquist–Johnson concrete (HJC) constitutive model of concrete, and the sensitive parameters of the HJC model are identified with A, B, G, Pl, μl, and fc respectively. LS‐DYNA nonlinear transient finite element analysis code was used for this paper. Based on the validation of finite element modeling and choosing midspan deflection of RC beams and impact loads as response indices, some influencing factors on RC beams under falling weight impact were investigated, such as the mass and speed of falling weight, impact position, the strength of concrete and rebar, longitudinal reinforcement ratio, and the span of the beam.

A study on the dynamic structural behavior of Olympic sabres

Sabres used in Olympic fencing are subject to severe elastic deformations during matches and training sessions. Even though strict rules for their manufacturing are prescribed by the international fencing federation, with requirements in terms of geometrical constraints and material (steel) properties, nonetheless frequent unexpected ruptures are observed. These may cause injuries to the fencers, and involve the replacement of the blade. In this study an experimental-numerical approach is adopted to investigate the underlying failure mechanisms. To this purpose, several attacks, “bouts” in fencing, were live filmed during actual practice with digital cameras and a trajectory tracking analysis was performed on the most critical of them, taking advantage of markers fixed on the blades at different positions. The post-processed data were subsequently used as boundary conditions of a 3D finite element model of the blade. Running a non-linear transient analysis, global and local quantities such as maximum stored elastic energy, stress and strain states, strain rates and possible permanent plastic strains were evaluated. A validation of the FE model with experiments was also carried out. From the critical analysis of experimental and numerical results it was possible to speculate about the influence of materials and dynamic related effects on the structural behavior of the blade. Eventually, hypotheses on fracture mechanisms were formulated.

Nonlinear transient analysis of FG pipe subjected to internal pressure and unsteady temperature in a natural gas facility

This study investigates the response of functionally graded (FG) gas pipe under unsteady internal pressure and temperature. The pipe is proposed to be manufactured from FGMs rather than custom carbon steel, to reduce the erosion, corrosion, pressure surge and temperature variation effects caused by conveying of gases. The distribution of material graduations are obeying power and sigmoidal functions varying with the pipe thickness. The sigmoidal distribution is proposed for the 1st time in analysis of FG pipe structure. A Two-dimensional (2D) plane strain problem is proposed to model the pipe cross-section. The Fourier law is applied to describe the heat flux and temperature variation through the pipe thickness. The time variation of internal pressure is described by using exponential-harmonic function. The proposed problem is solved numerically by a two-dimensional (2D) plane strain finite element ABAQUS software. Nine-node isoparametric element is selected. The proposed model is verified with published results. The effects of material graduation, material function, temperature and internal pressures on the response of FG gas pipe are investigated. The coupled temperature and displacement FEM solution is used to find a solution for the stress displacement and temperature fields simultaneously because the thermal and mechanical solutions affected greatly by each other. The obtained results present the applicability of alternative FGM materials rather than classical A106Gr.B steel. According to proposed model and numerical results, the FGM pipe is more effective in natural gas application, especially in eliminating the corrosion, erosion and reduction of stresses.

Numerical and experimental investigations of the low velocity impact in GFRP plates

Abstract The paper deals with experimental and numerical investigations of the composite plate subjected to low velocity impact (LVI). The discussed plates were made of eight-layer Glass Fiber Reinforced Polymer (GFRP) laminate with quasi-isotropic ply system and are predefined to conduct the impact and the Compression After Impact (CAI) tests. The numerical analyses were performed in Ansys® environment. Three numerical models were prepared. The implicit analyses were conducted with and without the implementation of the progressive failure algorithm and the application of the bilinear traction-separation law. The analyzed problem demonstrated the influence of the element-level time-incrementation, damping and time integration method (Newmark and Hilber-Hughes-Taylor) on agreement with the experimental results. The advantages of using impact constraints for modeling contact in a nonlinear transient dynamic analysis were shown. High consistency of numerical and experimental results was achieved. Application of the Hashin's criterion lead to a valid prediction of the fiber failure areas and to overestimation of the matrix failure areas.

Nonlinear static and transient isogeometric analysis of functionally graded microplates based on the modified strain gradient theory

The objective of this study is to develop an effective numerical model within the framework of an isogeometric analysis (IGA) to investigate the geometrically nonlinear responses of functionally graded (FG) microplates subjected to static and dynamic loadings. The size effect is captured based on the modified strain gradient theory with three length scale parameters. The third-order shear deformation plate theory is adopted to represent the kinematics of plates, while the geometric nonlinearity is accounted based on the von Kármán assumption. Moreover, the variations of material phrases through the plate thickness follow the rule of mixture. By using Hamilton’s principle, the governing equation of motion is derived and then discretized based on the IGA technique, which tailors the non-uniform rational B-splines (NURBS) basis functions as interpolation functions to fulfil the C2-continuity requirement. The nonlinear equations are solved by the Newmark’s time integration scheme with Newton-Raphson iterative procedure. Various examples are also presented to study the influences of size effect, material variations, boundary conditions and shear deformation on the nonlinear behaviour of FG microplates.

Non Linear Analysis on Multi Lobe Journal Bearings

Multi lobe journal bearings are used in machines which operate at high speeds and high loads. In this paper the multi lobe bearing are analyzed to determine the effect of surface roughness during non linear loading. A non-linear time transient analysis is performed using the fourth order Runge Kutta method. The finite difference method is used to predict the pressure distribution over the bearing surface. The effect of eccentric ratio is studied and the variation of attitude angle is discussed. The journal center trajectories were calculated and plotted.

Probabilistic analysis method of turbine blisk with multi-failure modes by two-way fluid-thermal-solid coupling

This study develops multi-extremum response surface method (MERSM) for the probabilistic analysis of aeroengine turbine blisk with the coexistence of many failure modes by considering two-way fluid-thermal-solid coupling under complex working condition. The mathematical model of MERSM was established with respect to the random input variables of inlet temperature, inlet velocity, density of material, and rotor speed, and the output responses of the maximum values of deformation, stress, and strain. The comprehensive probabilistic analysis of turbine blisk was completed based on MERSM. The results demonstrate that the comprehensive reliability degree of turbine blisk is 0.9944 when the allowable deformation, stress, and strain are 2.6 × 10−3 m, 1.26 × 109 Pa, and 6.75 × 10−3 m/m, respectively. The main factors influencing the comprehensive reliability degree of turbine blisk are rotor speed and gas temperature. The secondary factors are inlet velocity and density of material. As revealed from the comparison of methods, MERSM improves the computational speed and efficiency with the guarantee of accuracy. The efforts of this paper provide a promising approach for the nonlinear transient reliability analysis of complex structures with multi-failure modes and two-way fluid-thermal-solid coupling.

Stability of Flexibly supported Finite Oil Journal Bearings including Fluid Inertia and surface Roughness Effect: A Non-linear Transient Analysis

Stability of Flexibly supported Finite Oil Journal Bearings including Fluid Inertia and surface Roughness Effect: A Non-linear Transient Analysis

Nonlinear Transient Modeling and Design of Turbocharger Rotor/Semi-Floating Bush Bearing System

This work presents the bearing design and analysis of radial semi-floating bush oil lubricated bearings for a typical industrial turbocharger configuration. Initially, the stability analysis for a linear rotor/bearing system is evaluated through eigenvalues and eigenvectors. The stiffness and damping coefficients of the inner oil film are obtained for the linear modeling process. The operating speed range of the turbocharger is high enough, at 21,000 to 24,000 rpm, to be unstable, indicating that the analysis should be and is carried out with nonlinear transient modeling. The nonlinear transient analysis evaluates the rotor and bush limit cycle orbits, rotor dynamics, the forces acting on the rotor and semi-floating bush surfaces, the oil flow through the bearing, the oil temperatures, and the power loss of the two oil films. The optimum design of a set of semi-floating bush bearings for this application depends strongly upon the clearances of the bush and squeeze film damper, usually expressed as the non-dimensional clearance to radius ratio. A typical clearance is evaluated to determine the bearing performance in terms of orbit size, forces acting on the bush and squeeze damper surfaces, oil flow through the bearing, power loss, and thermal heating. The nonlinear transient orbit values are evaluated for frequency content using the FFT to determine which orbits show both the synchronous and sub-synchronous vibration components and the associated rotor modes excited. These results are compared to the linear analysis over the operating speed range. The oil flow through the bearing component is much larger than the squeeze film damper. The forces acting on the bush and squeeze damper surfaces are related to the fatigue life of the bearing.

Innovative Design of Fire Doors: Computational Modeling and Experimental Validation

Usually the design of fire doors is carried out to fulfil thermal requirements only, whereas also thermal distortion could significantly affect the safety behavior of the door. Indeed, the door tends to bend away from its supporting frame due to a non-uniform temperature distribution, which could lead to flame and smoke propagation. In this work an innovative design scheme is proposed, where the mechanical response of the door is enhanced without affecting its insulating properties. This improvement is achieved by changing the disposition of the constitutive elements (insulating material and structural plates). The behavior of a conventional and of an innovative door during a fire test was simulated with three-dimensional (3D) finite element models. A non-linear thermo-mechanical transient analysis was performed as well. The numerical results were validated with an experimental campaign made on true scale specimens, where the doors were heated by a furnace reaching a maximum temperature of 950°C. The temperature distribution was measured with several thermocouples and an infrared camera, whereas displacements were monitored with a laser sensor. It was observed that, while temperatures on the unexposed surface were around 120°C in both cases, the maximum out-of-plane displacement measured in the innovative door was 3 times smaller than that of the conventional configuration.

Structural response analysis of slamming impact on free fall lifeboats

The evaluation of impact induced slamming loads experienced by ships and offshore structures using advanced fluid structure interaction methods may be a challenging task involving complex and time consuming engineering solutions. This is the reason why to date the application of well understood and validated quasi-response approaches remains the most rational alternative used by experts for preliminary design assessment. Based on a benchmark study carried out by the International Ship and Offshore Structures Congress Technical Committee II.1 on Quasi-Static Response this paper demonstrates the practical use of “quasi-response” prediction methods for the assessment of impact loads on modern free fall lifeboats. The case study presented is considered relevant in terms of technical background and ship design for safety. Following a brief review rationalising the practical relevance of the engineering solutions examined, the influence of high speed impact is evaluated using linear-elastic and nonlinear beam models, as well as a nonlinear transient dynamic finite element analysis idealisation. Comparisons of the methods presented against experimental results led to the conclusion that the nonlinear quasi-dynamic beam approach accounts for the influence of the dynamic effects of strain by suitably idealising the effects of nonlinear geometric stiffness. It may therefore be more appropriate to employ this approach at preliminary stage, especially when conducting comparisons against simplistic linear methods used for rigid structures (e.g. stiffened steel and aluminium panels), or advanced nonlinear finite element analysis and other multi-physics methods that may be computationally complex and time consuming.

Reply to Giannakos, K. Comment on: Toughness of Railroad Concrete Crossties with Holes and Web Openings. Infrastructures 2017, 2, 3

This paper responds to the discussion [1] by Dr. K. Giannakos over our technical note [2].[...]