Nonlinear Kinematic Research Articles

Investigating Morison Modeling of Viscous Forces by Steep Waves on Columns of a Fixed Floating Offshore Wind Turbine (FOWT) Using Computational Fluid Dynamics (CFD)

Mean and slowly varying wave loads on floating offshore wind turbines (FOWTs) need to be estimated accurately for the design of mooring systems. The low-frequency drift forces are underestimated by potential flow theory, especially in steep waves. Viscous forces on columns is an important contributor which could be included by adding the quadratic drag of Morison formulation to the potential flow solution. The drag coefficients in Morison equation can be determined based on an empirical formula, CFD study, or model testing. In the WINDMOOR project, a FOWT support structure, composed of three columns joined at the bottom by pontoons and at the top by deck beams, is studied using CFD. In order to extract the KC-dependent drag coefficients, a series of simulations for the fixed structure in regular waves is performed with the CFD code STAR-CCM+. In this study, the forces along each column of the FOWT are analyzed using the results of CFD as well as potential flow simulations. The hydrodynamic interactions between the columns are addressed. A methodology is proposed to process the CFD results of forces on the columns and extract the contribution of viscous effects. Limitations of the Morison drag model to represent extracted viscous forces in steep waves are investigated. The obtained drag coefficients are compared with the available data in the literature. It is shown that accounting for potential flow interactions and nonlinear flow kinematics could, to a large degree, explain the previously reported differences between drag coefficients for a column in waves. Moreover, it is shown that the proposed model can capture the contribution of viscous effects to mean drift forces for fixed columns in waves.

Proposing a New Crack Driving Force Parameter for Fatigue Crack Growth Rate of C–Mn Steel

ABSTRACTThe present study is aimed at analyzing the fatigue crack growth rate data on compact tension (CT) and three‐point‐bend (TPB) specimens of C–Mn steel under different positive load ratios. Detailed elastic–plastic finite element analyses have been performed using nonlinear kinematic hardening rule of Chaboche material model. The numerically calculated plastic zone ahead of crack tip has been compared with measured plastic zone using digital image correlation technique. The fatigue crack growth rate curves have been analyzed with respect to different crack driving forces such as (i) single‐parameter stress intensity factor (SIF) range, (ii) two‐parameter‐based SIF (), and (iii) cyclic plasticity zone–based models. A new crack driving force has been proposed considering cyclic plastic zone and representative plastic strain accumulation within this zone. The parameter and proposed model resulted in improved assessments for different load ratios and constraint geometries (CT and TPB).

Consideration of Rocking Wind Turbine Foundations on Undrained Clay with an Efficient Constitutive Model

The concept of rocking foundations has been successfully tested and promoted for building and bridge foundations. In this paper, the applicability of rocking foundations to wind turbines is investigated, specifically for wind turbines constructed on undrained clay. An efficient form of von Mises constitutive model with non-linear kinematic hardening is integrated with the ABAQUS finite element software by a computer code and validated against experimental data. A cohesive contact of foundation–soil with limited tension is applied to simulate suction stresses at the foundation bottom–soil interface, which better represented the rocking foundation behavior. The obtained finite element results demonstrate that by allowing minimal foundation uplift under operational loads, an existing foundation can be used to support loads from a larger wind turbine than it is designed for. Allowing such uplifts corresponds to a rocking foundation design that is demonstrated in this paper to be safe and functional for a wind turbine under both operational and extreme conditions.

CALIBRATION OF CHABOCHE KINEMATIC HARDENING MODEL PARAMETERS BY OPTIMISATION

Drag links are used in the automotive industry mostly, and during painting, their ends are protected against paint by two types of cap productions. While one is machined, the other is cold formed. In this study, a finite element simulation for the deformation process of a drag link’s cap made from St52 alloy is performed. For the plasticity model, Chaboche’s nonlinear kinematic hardening rule is used with the associated flow rule and Von Mises yield criterion. Chaboche’s parameters are determined by low cycle fatigue test by applying curve fitting methods to one hysteresis loop. Furthermore, the Chaboche model parameters are calibrated by the optimization process. The final diameters of the cap measurements are compared with those obtained from the optimized model. Therefore, a comprehensive methodology is presented for the determination and calibration of Chaboche kinematic hardening model parameters. Chaboches calibrated parameters are YS=370,73 MPa, C=3513,5 MPa, and =47,958 while their initial values are YS=360 MPa, C=3500 MPa, and =90.

Dual Approach to Large-Scale Seismic Vulnerability Assessment of Churches Through Representative Archetypes

In this paper, the seismic vulnerability of churches is assessed using different methods characterized by different levels of complexity depending on the accuracy of the results to be achieved. Specifically, we compare the two main types of methodologies applied in the literature, namely, empirical and analytical methods. Empirical methods assess seismic vulnerability based on engineering judgements. In this study, these evaluations were carried out through an automatic tool, the MACHRO form, which was introduced in the past by the authors with the purpose of making evaluations as objective as possible. Analytical methods evaluate the vulnerability of a stock of churches through linear and nonlinear kinematic analyses performed for the most vulnerable macro-elements, which are treated by means of mechanical models. When the number of churches in the stock is huge, this type of evaluation might prove unfeasible. For this reason, churches are grouped into a manageable number of archetypes in order to be analyzed. The above-described methodologies were applied to a relevant number of churches, aiming to appraise discrepancies in terms of results and highlight advantages and drawbacks of their application.

Design and kinematic analysis of cable-driven underactuated manipulator on spacecraft

Cable-driven manipulators present significant dexterity and compliance in highly complex environments, which shows potential advantages for its application in the aerospace engineering. However, the application of the manipulators is still constrained by their inherent limitations, such as the large size and mass of the driving base, low load capacity and nonlinear complex models. In this paper, we design a novel cable-driven underactuated manipulator (CDUM) with high load capacity and less actuator motor, and propose a multi-level kinematic model for the proposed CDUM. The CDUM with 7 degrees of freedom is driven by three motors, which is composed of two segments. The segment 2 is capable of both telescoping and rotational movements, which is driven by two cables. To enhance its load capacity, a novel worm joint is designed for segment 1. Moreover, the joints of each segment can move with equal rotation angle and translational displacement by utilizing synchronous mechanism. Based on the structural features of the manipulator, the multi-level kinematics from the actuator variables to manipulator end-effector are expounded, including the actuator-joint kinematics and joint-end kinematics. Especially, the decoupled kinematic equation is derived to illustrate the coupling motion principle between joint variables of a single joint of segment 2. Finally, computational simulations are conducted to analyze the performance of the proposed mechanism and verify the method proposed in this work. The numerical results demonstrate that the cable-driven manipulator moves smoothly and the proposed nonlinear kinematics model is effective.

A Simple Geometrically Exact Displacement Based Shell Finite Element

This paper presents a modification of the T6-3iKL element based solely on displacements. It is a nonconforming triangular element with 6 nodes and a quadratic displacement field enhanced by a bubble function. Its coefficients are eliminated with three scalar rotation parameters at the mid-side nodes. The element approximates the Kirchhoff-Love shell model in the large displacement domain with only 21 DoFs . The rotation-continuity between adjacent elements is enforced at mid-side nodes, allowing for multiple branch connections in the mesh. The element allows the adoption of different material constitutive equations. The model is numerically implemented, and the results are compared to varying references in multiple examples, showing the capabilities of the formulation. The original desirable properties of the T6-i3KL element are preserved, which are the lack of penalties or Lagrange multipliers, a simple exact nonlinear kinematics, a relatively small number of DoFs, the possibility of using 3D material models, and is easily connected with multiple branched shells and beams.

A novel combined hardening rule for the brass cartridge case using crimping simulation and optimization

A cartridge shell case, a critical component in the defence industry, undergoes a crimping process to form one end for the insertion of a bullet. The shell case is primarily composed of brass. The crimping process is simulated using a novel plasticity model that combines a hardening rule with the Hill48 yield criterion and the associated flow rule. This study focuses primarily on the hardening rule, where a bilinear isotropic hardening (BISO) and Chaboche's nonlinear kinematic hardening (CHAB) rules are combined to develop a novel hardening model. The raw parameters of the models are calculated by regression performed on the data from monotonic tensile test and low-cycle fatigue (LCF) test. A multi-objective genetic algorithm is used to calibrate the raw parameters by the inverse analysis. The performance of the models is evaluated on the diameter of the shell considering the work-hardening. The novelty of this study lies in the acquisition of calibrated hardening rule parameters for the crimping process, which involves a multi-axial deformation pattern, using only data from uniaxial tensile and LCF tests, which are simpler to conduct. The force-moment requirements, springback, and material flow path are also calculated. The results provide a valuable insight into the combined hardening model, its parameters, and their sensitivity for the crimping process. The calibration process results in significant improvements in material properties, particularly yield strength ( YS) and tangent modulus ( TM). For the crimping, YS is observed to increase by 37.82% and TM is observed to decrease by 13.84% while parameters [Formula: see text] increase approximately 9% where Cm is hardening modulus, and [Formula: see text] is decrease rate. The model achives an absolute percent relative error (APE) of 0.18%.

Phase Field Coupled Finite Deformation Plasticity Formulation of Ductile Fracture With Nonlinear Kinematic Hardening and Modified Energy Release Function

ABSTRACTA ductile damage theory is presented by coupling the covariant formulation of finite deformation plasticity with the phase field modeling of fracture, including kinematic hardening for the ductile response of the materials. A phase field coupled nonlinear kinematic hardening equation is proposed in the reference configuration having equivalent representation through the Lie derivative of the kinematic hardening tensor by push‐forward operation in the spatial configuration, thus ensuring the satisfaction of frame invariance. To capture the correct physical response of the material by the phase field evolution equation, the fracture driving function, that is, the difference between the sum of elastic and plastic energies and threshold energy, after the damage initiation is modified by an energy release controlling function, which is an empirical relation of equivalent plastic strain. In defining the energy release controlling function, well‐defined points with physical significance in the experimental load versus displacement curve are used. To simulate the response of the material in relatively large time steps, a modified staggered scheme is presented, evaluating the fracture driving and energy release controlling functions from the previous converged step and using the updated phase field variable in the weak form of the momentum balance equation. To quantify different material parameters from available experimental results in the literature, the developed phase field coupled elasto‐plastic model uses a neural network optimization procedure consisting of neural network training together with optimization in MATLAB and finite element model evaluation in Abaqus user element subroutine UEL. Model capabilities are demonstrated by simulating the crack propagation in complex 3D geometries such as the second and third Sandia Fracture Challenges.

Discrete macro - models of nonlinear interlocking mechanisms in the out-of-plane failure of masonry walls

AbstractHistorical unreinforced masonry (URM) constructions are generally vulnerable to out-of-plane (OOP) failures due to the absence of rigid floors and poor connections between orthogonal walls. That leads to the activation of rocking mechanisms of external walls, whose ultimate force and displacement are affected by complex nonlinear interactions with sidewalls. These interactions are often neglected in the engineering practice, potentially leading to significant approximations, as demonstrated by experimental and numerical studies available in the literature. As a novel contribution to the field, this paper presents an upgraded discrete macro-element model (DMEM) to predict the rocking capacity of OOP loaded URM walls interacting with sidewalls. Considering both the onset and the evolution of the rocking mechanism of the front wall, interlocking effects with the sidewalls are first simulated through frictional resistances using the macro-block model (MBM) and the nonlinear kinematic approach of limit analysis. Then, the upgraded DMEM is implemented on the basis of the equivalence between the continuous distribution of these forces, introduced as a further novelty of the paper, and the discrete distribution of lateral elastic-plastic links, accounting for mechanical and geometrical nonlinearities. The results of the two models are discussed in terms of both frictional resistance-displacement and pushover curves, referring to a case study of a front wall belonging to a two-storey URM building. The wall response is also compared with the results derived from the original source of the case study and analysed by changing the number of nonlinear links to define different levels of accuracy.

Multiquadric Collocations for Nonlinear Vibration of Functionally Graded Plates of Ti–6Al–4V Metal

While Finite Element Method (FEM) has proven reliable for analyzing linear or nonlinear stresses in materials, structures, and fluid flows, its reliance on mesh generation can escalate project simulation costs. In contrast, mesh- free techniques offer an alternative by directly generating system algebraic equations for the entire issue domain, bypassing the need for a preset mesh. This study focuses on investigating the nonlinear free vibration response of shear-deformable Functionally Graded Material (FGM) plates. These plates are expected to exhibit varying material properties, following a power-law distribution linked to the volume fractions of constituent materials as plate thickness increases. Utilizing shear deformation theories and von Karman nonlinear kinematics, the study seeks a mathematical solution for the real physical issues encountered in these plates. To address these challenges, a meshless method employing the Multi Quadric Radial Basis Function (MQRBF) is employed for evaluation. The computed results reveal insights into how different material properties and amplitudes influence the nonlinear free vibration response of composite plates. Comparing these outcomes to prior research demonstrates promising progress in this area.

Tunable High-Static-Low-Dynamic Stiffness Isolator under Harmonic and Seismic Loads

High-Static-Low-Dynamic Stiffness (HSLDS) mechanisms exploit nonlinear kinematics to improve the effectiveness of isolators, preserving controlled static deflections while maintaining low natural frequencies. Although extensively studied under harmonic base excitation, there are still few applications considering real seismic signals and little experimental evidence of real-world performance. This study experimentally demonstrates the beneficial effects of HSLDS isolators over linear ones in reducing the vibrations transmitted to the suspended mass under near-fault earthquakes. A tripod mechanism isolator is presented, and a lumped parameter model is formulated considering a piecewise nonlinear–linear stiffness, with dissipation taken into account through viscous and dry friction forces. Experimental shake table tests are conducted considering harmonic base motion to evaluate the isolator transmissibility in the vertical direction. Excellent agreement is observed when comparing the model to the experimental measurements. Finally, the behavior of the isolator is investigated under earthquake inputs, and results are presented using vertical acceleration time histories and spectra, demonstrating the vibration reduction provided by the nonlinear isolator.

Adaptive sliding-mode delay compensation for real-time hybrid simulations with multiple actuators

Real-time hybrid simulation (RTHS) is a widely applied test method in structural engineering, which is developed from pseudo-dynamic test. Much of the past work has been centered on one-dimensional RTHS using a single hydraulic actuator. When the complexity of the problem demands to increase the number of degrees of freedom to be enforced on the boundary conditions, more than one hydraulic actuator must be used. Multiple-actuator or multi-axial RTHS (maRTHS) requires that more than one hydraulic actuator exerts the required motion on experimental substructures demanding the implementation of multiple-input multiple-output (MIMO) control strategies. A new maRTHS benchmark control problem has been developed, focusing on a frame subjected to seismic load at the base, substantially transforming and intensifying the complexity of the problem. The time delay generated by the dynamic characteristics of the loading system and the transmission process as well as the high coupling between the hydraulic actuators and the nonlinear kinematics escalates the complexity of the actuator control tracking. A sliding mode adaptive delay compensation method suitable for maRTHS is proposed, which utilizes a MIMO sliding mode method to reduce the coupling effects of actuators and the adaptive compensation method to compensate the residual delay. The effectiveness of the method is verified by numerical simulating different working conditions in the Benchmark Problem Platform.

Postbuckling behaviour of anisotropic shear deformable laminated cylindrical shells with general imperfection distribution subjected to torsion

Postbuckling behaviour of anisotropic shear deformable laminated cylindrical shells with general imperfection distribution subjected to torsion

Koiter–Newton Reduced-Order Method Using Mixed Kinematics for Nonlinear Buckling Analysis

The Koiter–Newton method improves the computational efficiency of nonlinear buckling analysis; however, the construction of reduced-order models using fully nonlinear kinematics is still a tedious and time-consuming work. In this paper, the Koiter–Newton reduced-order method using mixed nonlinear kinematics is presented for the geometrically nonlinear buckling analysis of thin-walled structures. Strain energy variations up to the fourth order were achieved using mixed kinematics for the improved Koiter theory. Corotational kinematics, which is inconvenient for high-order variations, was applied to calculate the first- and second-order variations for the internal force and tangent stiffness, respectively, whereas the third- and fourth-order strain energy variations were facilitated by explicit algebraic formulations using updated von Kármán kinematics. A reduced-order model with 1+m degrees of freedom was established, of which m perturbation loads were considered to make the method applicable for buckling problems. The geometrically nonlinear response was traced using a predictor–corrector strategy by combining the nonlinear prediction solved by the reduced-order model and the correction using Newton iterations. Numerical examples of structures with various buckling behaviors demonstrate that the performance of the proposed method is not obviously affected by using simplified kinematics, and sometimes it even exhibits a superior capability for path-following analysis.

Unsteady flow of nanofluid over a sheet of variable thickness with nonlinear kinematics

Unsteady flow of nanofluid over a sheet of variable thickness with nonlinear kinematics

Application of efficient algorithm based on block Newton method to elastoplastic problems with nonlinear kinematic hardening

PurposeThe purpose of this study is to present the effectiveness and robustness of a numerical algorithm based on the block Newton method for the nonlinear kinematic hardening rules adopted in modeling ductile materials.Design/methodology/approachElastoplastic problems can be defined as a coupled problem of the equilibrium equation for the overall structure and the yield equations for the stress state at every material point. When applying the Newton method to the coupled residual equations, the displacement field and the internal variables, which represent the plastic deformation, are updated simultaneously.FindingsThe presented numerical scheme leads to an explicit form of the hardening behavior, which includes the evolution of the equivalent plastic strain and the back stress, with the internal variables. The features of the present approach allow the displacement field and the hardening behavior to be updated straightforwardly. Thus, the scheme does not have any local iterative calculations and enables us to simultaneously decrease the residuals in the coupled boundary value problems.Originality/valueA pseudo-stress for the local residual and an algebraically derived consistent tangent are applied to elastic-plastic boundary value problems with nonlinear kinematic hardening. The numerical procedure incorporating the block Newton method ensures a quadratic rate of asymptotic convergence of a computationally efficient solution scheme. The proposed algorithm provides an efficient and robust computation in the elastoplastic analysis of ductile materials. Numerical examples under elaborate loading conditions demonstrate the effectiveness and robustness of the numerical scheme implemented in the finite element analysis.

Non-linear buckling analysis of delaminated hat-stringer panels using variational asymptotic method

Non-linear buckling analysis of delaminated hat-stringer panels using variational asymptotic method

Calibration of a Hybrid Machine Tool from the Point of View of Positioning Accuracy

The development of machine tools in the last twenty years includes, among other things, the application of mechanisms with a non-linear kinematic structure as the mechanical basis of machines. This results in significant improvements in kinematic characteristics and problems related to non-linear dependencies of the accuracy of the drive elements and the realization of movement in the machine’s external coordinates. The paper presents an approach to machine tool calibration based on the original O-X glide mechanism based on the ISO 230-4 standard with the mono- and bi-directional compensation of systematic errors and adaptation to the specifics of the mechanism’s kinematics. A machine tool prototype was designed and built for the research presented in the paper. The obtained results indicate the possibility of applying the existing recommendations and standards for testing the accuracy of machine tools with the need to correct the methodology by using linear and non-linear kinematic structures in machine tools.

An efficient 3D finite element procedure for simulating wheel–rail cyclic contact and ratcheting

An efficient 3D finite element procedure for simulating wheel–rail cyclic contact and ratcheting