Incremental-iterative Method Research Articles

Cyclic loading behaviour of thick cylindrical vessels under creep deformation

Influence of creep on cyclic loading behaviour of thick cylindrical vessels is studied in this paper. The cyclic loading response of cylindrical vessels under load and deformation controlled cyclic loading is compared for the cases where creep is included and excluded. Kinematic hardening theory of plasticity based on the multi-linear Prager and Armstrong–Frederick models is assumed to evaluate the multi-axial non-linear strains in the plastic region. An iterative incremental method is proposed to solve the governing equations due to the non-linearity and load history dependency of the problem. Based on the obtained results an interaction diagram is proposed to predict ratcheting or shakedown behaviour of the thick cylindrical vessels.

연약지반 직렬 무한궤도 주행차량의 선회특성 연구

The principal objective of this paper was to evaluate the steering characteristics of a tandem tracked vehicle, each side of which features two tandem tracks, when crawling on extremely cohesive soft soil. The tandem tracked vehicle is assumed to be a rigid-body with 6-dof. The dynamic analysis program of the tandem tracked vehicle was developed via Newmark's method and the incremental-iterative method. A terra-mechanics model of extremely cohesive soft soil was implemented according to the relationships of normal pressure to sinkage, of shear resistance to shear displacement, and of dynamic sinkage to shear displacement. In order to simplify the characteristics of contact interaction between track segments and cohesive soft soil, the characteristics of soil are equated to the properties of intact soil. In an effort to evaluate the steering characteristics of a tandem tracked vehicle crawling on extremely cohesive soft soil, a series of dynamic simulations were conducted for a tandem tracked vehicle model with respect to the front and rear steering angle, the steering ratio, and the initial velocity.

Nonlinear forced vibration of damped plates coupling asymptotic numerical method and reduction models

This work concerns the computation of the nonlinear solutions of forced vibration of damped plates. In a recent work (Boumediene et al. in Comput Struct 87:1508---1515, 2009), a numerical method coupling an asymptotic numerical method (ANM), harmonic balance method and Finite Element method was proposed to resolve this type of problem. The harmonic balance method transforms the dynamic equations to equivalent static ones which are solved by using a perturbation method (ANM) and the finite element method. The numerical results presented in reference (Boumediene et al. in Comput Struct 87:1508---1515, 2009) show that the ANM is very efficient and permits one to obtain the nonlinear solutions with few matrix triangulation numbers compared to a classical incremental iterative method. However, putting a great number of harmonics (6 or greater) into the load vector leads to tangent matrices with a great size. The computational time necessary for the triangulation of such matrices can then be large. In this paper, reduced order models are proposed to decrease the size of these matrices and consequently the computational time. We consider two reduced bases. In the first one, the reduced basis is obtained by the resolution of a classical eigenvalue problem. The second one is obtained by using the nonlinear solutions computed during the first step of the calculus which is realized with the ANM. Several classical benchmarks of nonlinear damped plates are presented to show the efficiency of the proposed numerical methods.

Analysis of impact response and damage in laminated composite cylindrical shells undergoing large deformations

The impact behaviour and the impact-induced damage in laminated composite cylindrical shell subjected to transverse impact by a foreign object are studied using three-dimensional non-linear transient dynamic finite element formulation. A layered version of 20 noded hexahedral element incorporating geometrical non-linearity is developed based on total Langragian approach. Non-linear system of equations resulting from non-linear strain displacement relation and non-linear contact loading are solved using Newton-Raphson incremental-iterative method. Some example problems of graphite/epoxy cylindrical shell panels are considered with variation of impactor and laminate parameters and influence of geometrical non-linear effect on the impact response and the resulting damage is investigated.

NONLINEAR ANALYSIS OF PLANAR REINFORCED CONCRETE FRAMES USING FINITE ELEMENT METHOD

In this study, a beam-column element that can be used in nonlinear analysis of reinforced concrete frame systems has been developed. The finite element method has been used to model beam-column elements. Kent-Park's model is also employed to model the confined and unconfined concrete behavior. Geometric nonlinearity is also included to nonlinear analysis using geometric stiffness matrix. The solution of nonlinear equation is solved using an iterative-incremental method that is called qgeneralized displaced control method.q The results obtained from the developed method for two examples are compared with the results of the experiment studies which are available in the literature in order to show accuracy of the program.

Corotational Nonlinear Finite Element Formulation and Modeling of Electrostatically Actuated Microbeams

A complete nonlinear finite element model for coupled-domain microelectromechanical system devices with electrostatic actuation and squeeze film effect was developed. for this purpose, a corotational finite element formulation for the dynamic analysis of planer Euler-Bernoulli microbeams considering geometrical nonlinearities due to both large structural deformation and electrostatic actuation is developed. In this method, the internal forces due to deformation and residual stresses, the elemental inertias, and the damping effect of the squeeze-film are systematically derived by consistent linearization of the fully geometrically nonlinear beam theory using d'Alembert and the virtual work principles. An incremental-iterative method based on the Newmark direct integration procedure and the Newton-Raphson algorithm is used to solve the nonlinear dynamic equilibrium equations. Several numerical examples are presented and their results are compared with those found experimentally, which indicate a very close agreement.

Estimation of ultimate hull girder strength with initial imperfections

The estimation of the ultimate strength of the ship hull is very important for its structural safety against applied loads. Various methodologies have been developed to evaluate the ultimate hull girder capacity, for example Caldwell (1965), Paik and Mansour (1995), International Association of Classification Societies Common structural rules (IACS CSR, 2006), etc. These methods do not usually include initial imperfections like initial deflection and initial residual welding stresses in the plating between stiffeners. The IACS CSR, introduced in April 2006, suggest the analytical incremental-iterative method for determining ultimate strength estimation of ship hull, which ignores welding residual stresses. In the present study, the stress–strain relationship for stiffened plate given in IACS CSR method is extended to account for the initial imperfections. Our previous work (Vhanmane and Bhattacharya 2007) on the stress–strain relationship of plate between stiffeners under axial loads, including imperfections like initial deflection and initial residual welding stresses, is used to determine the effective width of attached plating. The proposed methodology is applied to six benchmark cases: a double hull very large crude carrier and a capesize bulk carrier under three different levels of imperfection (slight, average, and severe) for both initial deflection and residual stresses. The ultimate strengths thus obtained are compared with published results that use two different methods (idealised structural unit method and finite element analysis) and it appears that the proposed methodology is simple yet robust in estimating hull girder ultimate strength under initial imperfections.

Ultimate behavior and ultimate load capacity of steel cable-stayed bridges

The main purpose of this paper is to investigate the ultimate behavior of steel cable-stayed bridges with design variables and compare the validity and applicability of computational methods for evaluating ultimate load capacity of cable-stayed bridges. The methods considered in this paper are elastic buckling analysis, inelastic buckling analysis and nonlinear elasto-plastic analysis. Elastic buckling analysis uses a numerical eigenvalue calculation without considering geometric nonlinearities of cable-stayed bridges and the inelastic material behavior of main components. Inelastic buckling analysis uses an iterative eigenvalue calculation to consider inelastic material behavior, but cannot consider geometric nonlinearities of cable-stayed bridges. The tangent modulus concept with the column strength curve prescribed in AASHTO LRFD is used to consider inelastic buckling behavior. Detailed procedures of inelastic buckling analysis are presented and corresponding computer codes were developed. In contrast, nonlinear elasto-plastic analysis uses an incremental-iterative method and can consider both geometric nonlinearities and inelastic material behavior of a cable-stayed bridge. Proprietary software ABAQUS are used and user-subroutines are newly written to update equivalent modulus of cables to consider geometric nonlinearity due to cable sags at each increment step. Ultimate load capacities with the three analyses are evaluated for numerical models of cable-stayed bridges that have center spans of 600 m, 900 m and 1200 m with different girder depths and live load cases. The results show that inelastic buckling analysis is an effective approximation method, as a simple and fast alternative, to obtain ultimate load capacity of long span cable-stayed bridges, whereas elastic buckling analysis greatly overestimates the overall stability of cable-stayed bridges.

Investigation of Shear Response of Fibrous Reinforced Concrete Beams Using Incremental-Iterative Method

Investigation of Shear Response of Fibrous Reinforced Concrete Beams Using Incremental-Iterative Method

Dynamic responses of flexible-link mechanisms with passive/active damping treatment

This work presents a finite element formulation for non-linear transient dynamic analysis of adaptive beams. The main contribution of this work concerns the development of an original co-rotational sandwich beam element, which allows large displacements and rotations, and takes active/passive damping into account. This element is composed of a viscoelastic core and elastic/piezoelectric laminated faces. The latter are modeled using classical laminate theory, where the electromechanical coupling is considered by modifying the stiffness of the piezoelectric layers. For the core, a four-parameter fractional derivative model is used to characterize its viscoelastic dissipative behavior. Equations of motion are solved using an incremental-iterative method based on the Newmark direct time integration scheme in conjunction with the Grünwald approximation of fractional derivatives, and the Newton–Raphson algorithm.

Finite element method-based three-dimensional frictional contact analysis of turbocharger compressor

In the long-distance transport of material, turbocharger compressors are playing an important role. The impeller mounted onto the compressor shaft assembly via interference fit is one of the key components of a centrifugal compressor stage. The assembly creates a complicated frictional contact problem on the interface of the contacting parts when the rotating speed is high. A locomotive-type turbocharger compressor with 24 blades under combined centrifugal and interference-fit loading is used for the analysis. The finite element parametric quadratic programming method that was developed based on the parametric variational principle is used for the analysis of the stress distribution of three-dimensional frictional contact problem between the impeller and the shaft assembly. The advantages of the parametric programming method when compared with the conventional ones are that the penalty factors can be cancelled and the solutions can be obtained directly without tedious iterative procedures such as general incremental iterative method. The effects of fit tolerance, coefficient of friction, the wall thickness of the shaft sleeve, rotational speed, and the contact stress distribution on the contacting surfaces are discussed in section 2. It is found that non-uniform initial amount of interference in the structural design would avoid relative displacement generated and ensure uniformity of the contact stress. To assure the quality of press-fitting, the amount of interference between the shaft sleeve and the shaft should be controlled strictly to avoid the rapid increase of the contact stress. The results obtained play a key role in deciding the proper fit tolerance and improving design and manufacturing technology of the compressor impellers. The current study also provides an effective approach which achieves more reliable interference-fitted connections and more precise assembly accuracy with lower manufacturing cost in the structural design.

Numerical simulation of contact problems in vane machinery by a parametric quadratic programming method

Interference fits are widely used for connecting impeller and shaft assembly that are forced together slowly by pressing. The interference fit design ensures stable balance behavior and allows for positive contact between the impeller and shaft assembly throughout the range of operating speeds. In addition to maintaining radial contact, sufficient net radial interface pressure must remain in order to transmit torque when the rotational speed is very high. Therefore, the interference fit between the impeller and the shaft assembly is one of the most important factors influencing the performance of the turbo unit in the design of turbocharger compressor. A suitable fit tolerance needs to be considered in the structural design. A locomotive-type turbocharger compressor with 24 blades under combined centrifugal and interference fit loading is used for the analysis. The finite-element (FE) parametric quadratic programming (PQP) method developed based on the parametric variational principle (PVP) is used for the analysis of the stress distribution in the three-dimensional (3D) contact problem of impeller. The advantages of the parametric programming method compared with conventional approaches are that the penalty factors can be canceled and that solutions can be obtained directly without tedious iterative procedures such as the general incremental iterative method. To save time in the computation, a~multi-substructure technique is adopted for structural modeling. This not only simplifies the calculation, but also provides a convenient service for process computer-aided design (CAD) by means of FE simulation. The effects of the fit tolerance, coefficient of friction and rotational speed (centrifugal force), wall thickness of the shaft sleeve and the contact stress on the interference-fitting surfaces are studied in detail in the numerical computation. It is found that a nonuniform initial amount of interference in the structural design avoids the relative displacement generated and ensures uniformity of the contact stress. To assure quality of press-fitting, the amount of interference between the shaft sleeve and shaft should be strictly controlled to avoid the rapid increase of the contact stress. The numerical results demonstrate the high accuracy and good convergence of the algorithm presented here, which provides an effective approach that achieves more-reliable interference-fitted connections and more-precise assembly accuracy with lower manufacturing cost in the structural design.

Saw-tooth softening/stiffening - a stable computational procedure for RC structures

Over the past years techniques for non-linear analysis have been enhanced significantly via improved solution procedures, extended finite element techniques and increased robustness of constitutive models. Nevertheless, problems remain, especially for real world structures of softening materials like concrete. The softening gives negative stiffness and risk of bifurcations due to multiple cracks that compete to survive. Incremental-iterative techniques have difficulties in selecting and handling the local peaks and snap-backs. In this contribution, an alternative method is proposed. The softening diagram of negative slope is replaced by a saw-tooth diagram of positive slopes. The incremental-iterative Newton method is replaced by a series of linear analyses using a special scaling technique with subsequent stiffness/strength reduction per critical element. It is shown that this event-by-event strategy is robust and reliable. First, the model is shown to be objective with respect to mesh refinement. Next, the example of a large-scale dog-bone specimen in direct tension is analyzed using an isotropic version of the saw-tooth model. The model is capable of automatically providing the snap-back response. Subsequently, the saw-tooth model is extended to include anisotropy for fixed crack directions to accommodate both tensile cracking and compression strut action for reinforced concrete. Three different reinforced concrete structures are analyzed, a tension-pull specimen, a slender beam and a slab. In all cases, the model naturally provides the local peaks and snap-backs associated with the subsequent development of primary cracks starting from the rebar. The secant saw-tooth stiffness is always positive and the analysis always `converges`. Bifurcations are prevented due to the scaling technique.

Dynamic modeling of geometrically nonlinear electrostatically actuated microbeams (Corotational Finite Element formulation and analysis)

In this paper, a complete nonlinear finite element model for coupled-domain MEMS devices with electrostatic actuation and squeeze film effect is developed. For this purpose, a corotational finite element formulation for the dynamic analysis of planer Euler beams is employed. In this method, the internal nodal forces due to deformation and intrinsic residual stresses, the inertial nodal forces, and the damping effect of squeezed air film are systematically derived by consistent linearization of the fully geometrically nonlinear beam theory using d′Alamber and virtual work principles. An incremental-iterative method based on the Newmark direct integration procedure and the Newton-Raphson algorithm is used to solve the nonlinear dynamic equilibrium equations. Numerical examples are presented and compared with experimental findings which indicate properly good agreement.

Numerical analysis of composite plates with multiple delaminations subjected to uniaxial buckling load

In this paper the buckling and post-buckling behaviour of unidirectional and cross-ply composite laminated plates with multiple delaminations has been studied. Finite elements analyses have been performed, using a linear buckling model, based on the solution of the eigenvalues problem, and a non-linear one, based on an incremental-iterative method. With non-linear method large displacements have been taken into account and also contact constraints between sublaminates have been added to avoid their interpenetration. It has been found that both delamination length and position and stacking sequence of the plies influence the critical load of the plate; furthermore, linear and non-linear buckling models are not always in perfect agreement.

Co-rotational finite element formulation for thin-walled beams with generic open section

A consistent co-rotational total Lagrangian finite element formulation for the geometric nonlinear buckling and postbuckling analysis of thin-walled beams with generic open section is presented. The element developed here has two nodes with seven degrees of freedom per node. The element nodes are chosen to be located at the shear centers of the end cross-sections of the beam element and the shear center axis is chosen to be the reference axis. The deformations of the beam element are described in the current element coordinate system constructed at the current configuration of the beam element. The element nodal forces are derived using the virtual work principle. The virtual rigid body motion corresponding to the virtual nodal displacements is excluded in the derivation of the element nodal forces. A procedure is proposed to determine the virtual rigid body motion. The way used to determine the element coordinate system and element nodal deformations corresponding to the virtual nodal displacements and that corresponding to the incremental nodal displacement are consistent. In element nodal forces, all coupling among bending, twisting, and stretching deformations of the beam element is considered by consistent second-order linearization of the fully geometrically nonlinear beam theory. In the derivation of the element tangent stiffness matrix, the change of element nodal forces induced by the element rigid body rotations should be considered for the present method. Thus, a stability matrix is included in the element tangent stiffness matrix. An incremental-iterative method based on the Newton–Raphson method combined with constant arc length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations. The zero value of the tangent stiffness matrix determinant of the structure is used as the criterion of the buckling state. Numerical examples are presented to investigate the accuracy and efficiency of the proposed method. The effect of the terms in the element nodal force and tangent stiffness matrix, which will converge to zero with the decrease of element size, on the convergence rate of solution and accuracy for the buckling load and nonlinear behavior of three dimensional beam structures are also investigated through numerical examples.

Investigation of tooth contact deviations from the plane of action and their effects on gear transmission error

In this paper tooth contact deviations from the plane of action and their effects on gear transmission error are investigated. Tooth contact deviations come from intentional modification of involute tooth surfaces such as tip and root profile relief; manufacturing errors such as adjacent pitch error, profile errors, misalignment and lead errors; and tooth elastic deflections under load, for example, bending and local contact deflections. Those deviations are usually neglected on gear tooth contact models. A procedure to calculate the static transmission error of spur and helical gears under loading is proposed. In the proposed procedure, contact analysis is carried out on the whole tooth surface, eliminating the usual assumption that tooth contact occurs only on the plane of action. Lead and profile modifications, manufacturing errors and tooth elastic deflections are considered in the calculation procedure. The method of influence coefficients is employed to calculate the tooth elastic deflections. Load distribution on gear meshing is determined using an iterative-incremental method. Results of some numerical examples of spur and helical gears are analysed and discussed. The results indicate that the tooth contact deviations from the plane of action can lead to imprecision on the gear transmission error calculation if they are not take into account. Therefore, the proposed procedure provides a more accurate calculation methodology of gear transmission error, since a global contact analysis is done.

Contemporary type of analysis on contact problems with friction using the finite element approach

This paper elaborates theoretic methods which give solutions for nonlinear problems of contact with friction that arise from stick-slip phenomenon. The aim of the study is anticipation of tension and deformations on the contact surface as well as inside of components that come in contact, because contact surface is changing progressively owing to outer load induction. In this paper it is presumed that materials are linearly elastic, while motions and deformations are minor, and contact surface is continuous and plane. It is also presumed that it does not come to mutual perforation of the objects surfaces in contact. The paper is based on finite elements method, modified for contact problems, on iterative-incremental method and with contemporary mathematical theoretical assumption for contact problem solving.

The Incremental Gauss-Newton Algorithm with Adaptive Stepsize Rule

In this paper, we consider the Extended Kalman Filter (EKF) for solving nonlinear least squares problems. EKF is an incremental iterative method based on Gauss-Newton method that has nice convergence properties. Although EKF has the global convergence property under some conditions, the convergence rate is only sublinear under the same conditions. One of the reasons why EKF shows slow convergence is the lack of explicit stepsize. In the paper, we propose a stepsize rule for EKF and establish global convergence of the algorithm under the boundedness of the generated sequence and appropriate assumptions on the objective function. A notable feature of the stepsize rule is that the stepsize is kept greater than or equal to 1 at each iteration, and increases at a linear rate of k under an additional condition. Therefore, we can expect that the proposed method converges faster than the original EKF. We report some numerical results, which demonstrate that the proposed method is promising.

Simulating cyclic artery compression using a 3D unsteady model with fluid–structure interactions

High pulsating blood pressure and severe stenosis make fluid–structure interaction (FSI) an important role in simulating blood flow in stenotic arteries. A three-dimensional nonlinear model with FSI and a numerical method using GFD are introduced to study unsteady viscous flow in stenotic tubes with cyclic wall collapse simulating blood flow in stenotic carotid arteries. The Navier–Stokes equations are used as the governing equations for the fluid. A thin-shell model is used for the tube wall. Interaction between fluid and tube wall is treated by an incremental boundary iteration method. Elastic properties of the tube wall are determined experimentally using a polyvinyl alcohol hydrogel artery stenosis model. Cyclic tube compression and collapse, negative pressure and high shear stress at the throat of the stenosis, flow recirculation and low shear stress just distal to the stenoses were observed under physiological conditions. These critical flow and mechanical conditions may be related to platelet aggregation, thrombus formation, excessive artery fatigue and possible plaque cap rupture. Computational and experimental results are compared and reasonable agreement is found.