Rigid Finite Element Method Research Articles

WITHDRAWN: Visualized neural network-based vibration control for pigeon-like flexible flapping wings

This study investigates pigeon-like flexible flapping wings, which are known for their low energy consumption, high flexibility, and lightweight design. However, such flexible flapping wing systems are prone to deformation and vibration during flight, leading to performance degradation. It is thus necessary to design a control method to effectively manage the vibration of flexible wings. This paper proposes an improved rigid finite element method (IRFE) to develop a dynamic visualization model of flexible flapping wings. Subsequently, an adaptive vibration controller was designed based on non-singular terminal sliding mode (NTSM) control and fuzzy neural network (FNN) in order to effectively solve the problems of system uncertainty and actuator failure. With the proposed control, stability of the closed loop system is achieved in the context of Lyapunov’s stability theory. At last, a joint simulation using MapleSim and MATLAB/Simulink was conducted to verify the effectiveness and robustness of the proposed controller in terms of trajectory tracking and vibration suppression.The obtained results have demonstrated great practical value of the proposed method in both military (low-altitude reconnaissance, urban operations, and accurate delivery, etc.) and civil (field research, monitoring, and relief for disasters, etc.) applications.

Modelling 3D dynamics of offshore lattice jib cranes by means of the rigid finite element method

Offshore cranes require particularly careful design due to the difficult environmental conditions in which they work. This paper presents a 3D model of the dynamics of an offshore crane with a truss jib formulated by means of the rigid finite element method. The inertial features of the truss members are assigned to nodes whose rotational and translational displacements are degrees of freedom. Flexible features of the truss members are modelled by massless and dimensionless spring–damping elements (sde). The computer programme developed on the basis of the model is verified and validated, and good correspondence of the authors’ own results with those obtained using commercial FEM package is achieved. Computer simulations are carried out for the light crane used on the wind platforms. The influence of the base movements (sea waves) on the system are also investigated. Lifting a load from a supply vessel and the load on the system during rotational movement of the crane are simulated too. Finally, conclusions concerning the influence of the movement conditions on the overload coefficient and deflections of the crane boom are formulated.

Modelling and real-time dynamic simulation of flexible needles for prostate biopsy and brachytherapy

ABSTRACT Percutaneous needle insertion constitutes a widely adopted technique for performing minimally invasive operations. Robot-assisted needle placement and virtual surgical training platforms have the potential to significantly improve the accuracy of these operations. For this, the development of mathematical models that provide a complete characterization of the underlying dynamics of medical needles is considered of paramount importance. In this paper, we develop two three-dimensional nonlinear rigid/flexible dynamic models of brachytherapy and local anaesthetic transperineal biopsy (LATP) needles. The proposed models relax the assumptions of previous investigations, quantify the vibrational behaviour and the rigid-body dynamics of medical needles and allow for real-time haptic and visual feedback information. Their accuracy and computational efficiency are assessed and validated using commercial software. The results show that, among the examined methods, the Rigid Finite Element Method provides the most accurate and numerically efficient solution for capturing the dynamics of flexible medical needles.

Numerical investigation on the constraint violation suppression methods efficiency and accuracy for dynamics of mechanisms with flexible links and friction in joints

In this paper, a mathematical model of the spatial mechanism with a serial closed-loop structure composed of spherical, revolute and prismatic joints taking into account links’ flexibility and friction in joints is formulated. Two approaches of the Rigid Finite Element Method (classical and modified) are analysed in the context of constraints violations. Numerical efficiency and accuracy of the constraint violation suppression (CVS) methods are studied when friction in joints and links’ flexibility are taken into account. Advantages and drawbacks of these methods for selected ODE solvers are also discussed. The most suitable CVS methods dedicated for the spatial mechanism defined using the formalism of joint coordinates are proposed in the paper. General conclusions are given in the final part of the paper.

Adaptive Finite-Time Fault-Tolerant Control for Uncertain Flexible Flapping Wings Based on Rigid Finite Element Method

The bionic flapping-wing robotic aircraft is inspired by the flight of birds or insects. This article focuses on the flexible wings of the aircraft, which has great advantages, such as being lightweight, having high flexibility, and offering low energy consumption. However, flexible wings might generate the unexpected deformation and vibration during the flying process. The vibration will degrade the flight performance, even shorten the lifespan of the aircraft. Therefore, designing an effective control method for suppressing vibrations of the flexible wings is significant in practice. The main purpose of this article is to develop an adaptive fault-tolerant control scheme for the flexible wings of the aircraft. Dynamic modeling, control design, and stability verification for the aircraft system are conducted. First, the dynamic model of the flexible flapping-wing aircraft is established by an improved rigid finite element (IRFE) method. Second, a novel adaptive fault-tolerant controller based on the fuzzy neural network (FNN) and nonsingular fast terminal sliding-mode (NFTSM) control scheme are proposed for tracking control and vibration suppression of the flexible wings, while successfully addressing the issues of system uncertainties and actuator failures. Third, the stability of the closed-loop system is analyzed through Lyapunov's direct method. Finally, co-simulations through MapleSim and MATLAB/Simulink are carried out to verify the performance of the proposed controller.

A Novel Rigid Finite Element Formulation for Dynamic Analysis of Flexible Plates

This paper introduces a new rigid finite element method (RFEM) formulation for dynamic analysis of plates. In RFEM, a flexible body is divided into several rigid elements which are interconnected by spring and damping elements. Mainly, RFEM has been used to model systems with beam-like slender components, such as ropes and cables, and few RFEM formulations were developed to model plates and shells. In this study however, by means of the Timoshenko beam theory and cuboid rigid elements, a novel RFEM formulation is developed to model flexible flat plates with generic geometries of the surface, considering large deformation. For this purpose, an RFEM formulation is presented for straight beams with rectangular cross-section by means of the Timoshenko beam theory. Next, this formulation is expanded to model flexible rectangular plates with uniform thickness and then, it is elaborated on how to model non-rectangular plates with uniform thickness using only cuboid elements and consequently, the development of the proposed RFEM formulation is completed. After investigating various case studies, the competence of the proposed formulation is evaluated thoroughly. The results of RFEM came on a proper agreement with the FEM results in a way that the maximum difference between these results in dynamic analysis was about 3%.

Shape and Mass Optimization of the Connecting Rod using Rigid Body Dynamics and Finite Element Method

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.

Rigid finite element method in applications to dynamic optimization of motion of a riser in reentry

Overloading of a riser, with possible subsequent damage, can be caused when the bottom end of the suspended riser encounters an obstacle during its relocation realized in reentry. Such collisions can be avoided by appropriate horizontal and vertical displacements of the riser, which can be realized by planning the motion of the base or use of Heave Compensation Systems − HCS. Simulation tasks concerned with this problem can be solved by use of numerically effective models of a riser's dynamics and optimization methods. The model of dynamics of a riser presented in this paper and formulated by means of the rigid finite element method (RFEM) is validated against experimental measurements and calculation results presented by other researchers. Due to its very good numerical effectiveness, the model is then applied to the solution of two optimization problems. The first optimization task consists in choosing the horizontal displacements of the upper end of the riser so that the bottom end of the riser is positioned as closely as possible to the final position with reduced vibrations at the end of the base motion. In the second task the upper end of the riser is moved vertically in such a way that the bottom end of the riser stays at a safe distance from an obstacle during riser relocation. The results of optimization simulations for a number of cases are presented and discussed.

Multi Body Dynamic Equations of Belt Conveyor and the Reasonable Starting Mode

Based on the rigid finite element method and multibody dynamics, a discrete model of a flexible conveyor belt considering the material viscoelasticity is established. RFE (rigid finite element) and SDE (spring damping element) are used to describe the rigidity and flexibility of a conveyor belt. The dynamic differential equations of the RFE are derived by using Lagrange’s equation of the second kind of the non-conservative system. The generalized elastic potential capacity and generalized dissipation force of the SDE are considered. The forward recursive formula is used to construct the conveyor belt model. The validity of dynamic equations of conveyor belt is verified by field test. The starting mode of the conveyor is simulated by the model.

Modelling and parameter identification of steel\u2013concrete composite beams in 3D rigid finite element method

This study presents spatial vibration modelling of steel–concrete composite beams. Structures of this type are commonly used as elements of composite floors and primary carrying girders in bridge structures. Two-dimensional models used to date did not enable analysis of all eigenmodes, specifically torsional, flexural horizontal, and distortional. A discrete computational model was developed in the convention of the rigid finite element method, the so-called RFEM model. It was assumed that the concrete slab and the steel I-section would be modelled separately. This approach realistically reflects the actual performance of the connection, comprising studs connecting the concrete slab and the steel section. The model was used to analyse two steel–concrete composite beams with different connector spacings. The paper presents the results of experiments conducted on the two composite beams. Their dynamic characteristics, including frequency and vibration modes, were determined with impulse response methods. Based on experimental research, identification of connection parameters with substitute longitudinal moduli of elasticity of reinforced concrete was conducted. A comparison of experimental results with those calculated with the model confirmed their good agreement.

The influence of the PID controller settings on the motion of a truck-mounted crane with a flexible boom and friction in joints

The aim of the paper is to analyze the impact of the PID controller settings on the crane positioning accuracy. The PID controller is applied to minimize the load swingings during realization and after the ending of the working motion. In the proposed control system the tangent component of the load oscillations is compared with the assumed (leading) setpoint signal. The obtained controlling error is used to compensate for driving torque applied to the rotary column of crane. The controlled object in the considered control system is a truck-mounted crane. The paper presents a mathematical model of this crane. Dynamics equations are derived using the joint coordinates, homogeneous transformation matrices and the Lagrange equations of the second kind. The flexibility of the boom, supports, rope and drives as well as friction in joints are taken into account in the dynamics model. The Rigid Finite Element Method is applied to model the boom’s flexibility. The friction phenomenon in joints is modeled in the sense of the LuGre friction model. The numerical results obtained for the proposed control system at various controller settings are presented in the paper and discussed.

Dynamic analysis of flexible parallel robots via enhanced co-rotational and rigid finite element formulations

The aim of this paper is to develop formulations for the dynamic analysis of parallel robots considering the links flexibility. These formulations are based on two popular methods which are used frequently in the literature, the Co-rotational and Rigid finite elements. In the first part of this study, the co-rotational elements are incorporated to model the flexible links. Unlike the common co-rotational formulations presented in the literature, the deformation of each element is described directly in its co-rotated frame without the need of expressing any intricate kinematic relations. In the second part, a formulation based on the rigid finite element method is elaborated. The formulation simplifies the form and derivation of kinetic energy of a flexible link, with respect to the co-rotational elements, at the cost of assuming the elements to be rigid. Choosing the Delta parallel robot as a case study, the two aforementioned formulations are implemented and evaluated. The numerical simulations show that, for the same number of nodes, the results differed by 6% in the worst case. However, in terms of computational cost, the rigid finite element formulation always reduces the simulation time by 31%–46%.

Nonlinear dynamic modeling of ultrathin conducting polymer actuators including inertial effects

Trilayer conducting polymer (CP) actuators are potential alternatives to piezoelectric and electrostatic actuators due to their large strain, and recently demonstrated operation at hundreds of Hertz. However, these actuators exhibit nonlinear electrical and mechanical properties as a function of their oxidation state, when operated over their full strain range, making it more challenging to accurately predict their mechanical behavior. In this paper, an analytical multi-physics model of the CP actuators is proposed to predict their nonlinear dynamic mechanical behavior. To demonstrate the accuracy of the model, a trilayer actuator composed of a solid polymer electrolyte sandwiched between two poly(3,4-ethylenedioxythiophene) (PEDOT) electrodes was fabricated and characterized. This system consists of an electrical subsystem represented by an RC equivalent circuit, an electro-mechanical coupling matrix, and a mechanical subsystem described by using a rigid finite element method. The electrical conductivity and the volumetric capacitance, an empirical strain-to-charge ratio, and Young’s modulus of the actuator as a function of the PEDOT electrode charge state were also implemented into the model, using measured values. The proposed model was represented using a bond graph formalism. The concordance between the simulations and the measurements confirmed the accuracy of the model in predicting the nonlinear dynamic electrical and mechanical response of the actuators. In addition, the information extracted from the model also provided an insight into the critical parameters of the actuators and how they affect the actuator efficiency, as well as the energy distribution including dissipated, stored, and transferred energy. These are the key parameters for designing, optimizing, and controlling the actuation behavior of a trilayer actuator.

A 3D model for static and dynamic analysis of an offshore knuckle boom crane

The paper presents a spatial model of a crane consisting of two booms connected by means of a knuckle. Change of the crane radius and position of booms is realised by length change of cylinders. The crane model takes into account flexibility of booms, cylinders and the rope system. The rigid finite element method is used for discretisation of booms. The computer programme developed on the basis of the model presented enables calculations of dynamic and static analysis to be carried out. The software package is used by designers from PROTEA to test the crane during handling operations in conditions at sea. The model has been validated for tasks of lifting the load with a given velocity both from the air and base. Results of numerical simulations are compared with those of experimental measurements on the test stand.

Application of the Rigid Finite Element Method to Static Analysis of Lattice-Boom Cranes

In the paper a nonlinear model of a lattice-boom crane with lifting capacity up to 700mT for static analysis is presented. The rigid finite element method is used for discretisation of the lattice-boom and the mast. Flexibility of rope systems for vertical movement and for lifting a load is also taken into account. The computer programme developed enables forces and stress as well as displacements of the boom to be calculated. The model is validated by comparison of the authors’ own results with those obtained using professional ROBOT software. Good compatibility of results has been obtained.

A New Approach to the Rigid Finite Element Method in Modeling Spatial Slender Systems

The static and dynamic analysis of slender systems, which in this paper comprise lines and flexible links of manipulators, requires large deformations to be taken into consideration. This paper presents a modification of the rigid finite element method which enables modeling of such systems to include bending, torsional and longitudinal flexibility. In the formulation used, the elements into which the link is divided have seven DOFs. These describe the position of a chosen point, the extension of the element, and its orientation by means of the Euler angles Z[Formula: see text]Y[Formula: see text]X[Formula: see text]. Elements are connected by means of geometrical constraint equations. A compact algorithm for formulating and integrating the equations of motion is given. Models and programs are verified by comparing the results to those obtained by analytical solution and those from the finite element method. Finally, they are used to solve a benchmark problem encountered in nonlinear dynamic analysis of multibody systems.

Programmed task based motion analysis of robotic systems equipped with flexible links and supports

The automatic computational procedure to derivate dynamics equations of systems with programmed constraints modified to encompass compliant mechanical components in their structures is discussed in the paper. The dynamics analysis of the compliant manipulator model with a flexible link is presented as an example. The rigid finite element method is used in order to take into account the flexibility of the link. The formalism of joint coordinates and homogeneous transformations are used to describe the manipulator motion.

A Discrete-Continuous Method of Mechanical System Modelling

Abstract The paper describes a discrete-continuous method of dynamic system modelling. The presented approach is hybrid in its nature, as it combines the advantages of spatial discretization methods with those of continuous system modelling methods. In the proposed method, a three-dimensional system is discretised in two directions only, with the third direction remaining continuous. The thus obtained discrete-continuous model is described by a set of coupled partial differential equations, derived using the rigid finite element method (RFEM). For this purpose, firstly the general differential equations are written. Then these equations are converted into difference equations. The derived equations, expressed in matrix form, allow to create a global matrix for the whole system. They are solved using the distributed transfer function method. The proposed approach is illustrated with the examples of a simple beam fixed at both ends and a simply supported plate.

Natural frequency analysis and experiment for 3SPS+1PS parallel hip joint manipulator based on rigid-flexible coupling theory

For analyzing natural frequency of a 3SPS+1PS parallel hip joint manipulator, a rigid-flexible coupling theory is proposed. 3SPS denotes that the PHJM has three legs and each leg type is SPS. 1PS denotes that the PHJM has one constrained leg and the constrained leg type is PS. The rigid finite element method and flexible finite element method are the base of the rigid-flexible coupling theory. Firstly, the basic element models of the PHJM are established based on the rigid-flexible coupling analysis. Secondly, the elastic dynamic models of the flexible legs are established based on the Lagrange equation and flexible finite method. Finally, the rigid-flexible coupling model of the PHJM is assembled by building the relationship between the rigid and flexible elements. Based on the rigid-flexible model, the natural frequency of the PHJM is analyzed. In addition, the effect parameters of the natural frequency are analyzed. The analysis results of the natural frequency show that the natural frequency is symmetric distribution in the working space, and the minimum value of the 1st order natural frequency is 2.3 Hz. The operating frequency (1 Hz) is much lower than the 1st order natural frequency, so the PHJM will not generate resonance and can operate stably. The analysis results of the parameter show that the PHJM has the minimal sensitivity with the effect parameter E and has the maximal sensitivity with the effect parameter H, so the length of the middle leg has the biggest impact on the natural frequency. Natural frequency analysis results have been checked by the hammer test, which verifies the feasibility of the rigid-flexible coupling theory. At the same time, the regression analysis is carried out based on the hammer test results. Using the rigid-flexible coupling theory to solve the natural frequency of the parallel manipulator, the physical meaning is explicit and the modeling process is clear, so the rigid-flexible coupling theory is a universal method.

Application of dynamic optimisation to stabilise bending moments and top tension forces in risers

The study discusses the problem of determining vertical displacements of a riser’s ends, which, despite its horizontal displacements induced by waves, mitigate stresses. A spatial model of riser dynamics is presented that considers the geometric nonlinearity due to large deflections. The Rigid Finite Element Method was used for riser discretisation. Analyses are reported that enabled riser’s vibration frequency determination according to the positions of its upper and lower ends. Then a dynamic optimisation task was formulated and solved. It consists of the selection of riser’s vertical displacements that provide bending moments’ stabilisation at its selected points, tension forces, despite the defined horizontal movements of the riser’s upper end induced by waves. The calculations were performed for variable amplitudes of riser end’s horizontal movements.