Geometric Nonlinear Problems Research Articles

Research on ice shedding and broken conductor in tower-line system based on CR method

In cold climates, the damage to the transmission tower-line system is usually caused by ice shedding, broken conductors, and broken ground wires. To replicate the ice shedding and broken conductor scenarios more accurately and expeditiously within the transmission tower-line system, we have engineered a finite element computational program leveraging the co-rotational theory method, utilizing the C++ programming language. Additionally, we have orchestrated its visualization interface utilizing the QT and Visualization Toolkit (VTK) platforms. This program can accurately and rapidly simulate large displacement geometric nonlinear problems. An ice detachment criterion considering the resultant acceleration is proposed. Compared with previous judgment criteria, the criterion proposed in this article can adapt to the previous prediction accuracy and is more efficient in calculation. A finite element method for disconnection simulation of “node failure” was proposed, and its accuracy and computational efficiency were verified by comparison with experiments. By analyzing the coupling effect of disconnection and deicing in the tower line system, it is concluded that ground wires often have a stronger deicing effect than conductors. Although broken conductor will cause large-scale ice shedding from the span, the impact on the most dangerous point of the tower will be very small, this providing a theoretical basis for ice-covered broken conductor in the tower-line system. The simulation method proposed in this article also provides a new research idea for the simulation of ice shedding and broken conductor of tower-line systems.

Aeolian Vibration Dynamic Analysis of Large-Span, Relaxed Antenna Cable Net Based on Finite Particle Method

The large-span, relaxed antenna network is a large deformation flexible structure due to its low pre-tension level of the wires. Its dynamic analysis under a wind load belongs to dynamic and geometric nonlinear problems, which is very complex to accurately calculate and solve. This paper explores the possibility of the finite particle method (FPM) to the aeolian vibration analysis of a large-span, low stress-tensioned antenna cable net. In the FPM, the antenna network structure is discretized into a group of finite particles, where the motions of all particles follow Newton’s second law and can be solved dynamically using a central difference scheme. The effectiveness and applicability of the FPM were verified by comparing the calculation results of the finite element method and FPM. The FPM was used to study the effects of wind speed and the distribution of vibration on the aeolian vibration of antenna cable nets. The results showed that this method is suitable for studying the aeolian vibration of a large-span, low stress-tensioned antenna network and has high computational efficiency and accuracy.

Application of the FEM Method to Modeling and Analysis of the Cold Thread Rolling Process-Part 1: Conditions for Ensuring a Plane State of Deformations.

The article concerns the application of the FEM method for the prediction of stress and deformation states in a workpiece during the thread rolling process (TR). The analysis covered a new kinematic variant of the TR process in which the basket of the head rotates and is torque-driven, while the workpiece is stationary and the head with the rollers moves axially relative to the workpiece. The TR process was considered as a geometrical and physical non-linear initial and boundary problem with non-linear, moving, and variable in time and space boundary conditions. The boundary conditions in the contact areas of the tool with the workpiece were unknown. An updated Lagrange (UL) description was used to describe the physical phenomena at a typical incremental step. The states of strain and strain rate were described by non-linear relationships without linearization. New discrete systems of motion and deformation equations of the object in the TR were introduced, which take into account the change in the stiffness of the system during the TR process. This equation was solved by the central differences method (explicit). The material parameters were estimated during tensile tests to determine the characteristics of the C45 steel, and a new semi-empirical method was used to determine the relationship yield stress, effective true strain, and effective true strain rate in the thread rolling process. A modified Cowper-Symonds material model was also used to model the displacement process of the wedge on an elastic/visco-plastic body reflecting the TR process. A non-linear dependency of material hardening module depending on strain and strain rate was introduced. To confirm the plane state of deformation and spatial state of stress, an experimental investigation was carried out. The computer models were validated, and a good convergence of the results was obtained. Applications in the ANSYS/LS-Dyna program were developed to simulate the TR process. The developed applications enable a comprehensive time analysis of the states of displacement, strain, and stress occurring in an object consisting of a workpiece (shaft) and a tool (roller) for the case of a plane strain state and a spatial stress state. Exemplary results of numerical analyzes are presented to explain the influence of the friction coefficient on the condition of the thread quality, and the state of deformations and stresses were shown.

Geometric nonlinear transient analysis of mechanically and thermally shocked functionally graded shell panels

The present paper investigates the von-Karman geometrically nonlinear structural responses of ceramic-metal functionally graded shell panels under the effect of the cases of mechanical and thermal shocks on their ceramic-rich surface. The constituents in the FGM are temperature-dependent and are graded as per the recently proposed four-parameter power laws while their effective properties in the shells are obtained using the Mori-Tanaka homogenization scheme. The transient thermoelastic problem is solved by importing the temporally varying temperature distribution from the nonlinear 1D heat equation as thermal loads into the FE code developed for thin and moderately thick shells based on higher-order shear deformation theory. The nonlinearity in the heat equation is linearized using Picard method in each Crank-Nicholson time-step while the linearization step in the geometric nonlinear problem uses Newton-Raphson method in each Newmark time-step. The new results presented in the manuscript study the effect of geometric nonlinearity on the responses of FG shell panels and the effect of different parameters of four-parameter FG laws. It was observed that including geometric nonlinearity significantly affects the responses of the shell panel structures when the loading direction, either mechanical or thermal, along with the gradation direction is reversed.

Intrawell and interwell oscillations for bi-stable cross-ply laminates actuated by MFC under oscillating impulse voltages

The snap-through is a typical geometric nonlinear problem for the bi-stable laminate structures. Using the Macro Fiber Composite (MFC) actuators to actuate the snap-through behavior of the morphing structures has attracted considerable attention. In this paper, the intrawell oscillations and interwell oscillations are studied for the asymmetric four layers cross-ply bi-stable rectangular laminate actuated by the d33 type MFC actuator. It is assumed that the four edges of the bi-stable laminate are free while the geometry center of it is fixed. On the basis of the classical laminated plate theory and the Hamilton’s principle, the equations of motion of the bi-stable laminate which are expressed by curvatures are presented. The stable equilibrium configurations of the bi-stable laminate considering the effects of MFC are given. Under the action of oscillating impulse voltages, the intrawell oscillations and interwell oscillations of the system are analyzed in detail through the frequency-response curves, time response and the phase portraits. The numerical results show that the snap-through behavior is easier to realize for the bi-stable laminate actuated by the oscillating impulse voltages than that actuated by the static voltages. Furthermore, snap-through behavior can be better controlled by changing the amplitude and frequency of the applied voltages in a certain range.

A refined hyperbolic shear deformation theory for nonlinear bending and vibration isogeometric analysis of laminated composite plates

In this paper, a refined hyperbolic tangent higher order shear deformation theory is developed. Assuming that the shear function is parameter dependent, the parameters are determined by the inverse method. The refined theory is assessed by using the NURBS based isogeometric analysis for the geometric linear and nonlinear bending and free vibration problems of laminated composite plates. The nonlinearity of the plates is based on the von-Karman strain assumptions. Numerical examples show that the refined hyperbolic tangent shear deformation theory combined with IGA has high accuracy in both linear and geometric nonlinear analysis of laminated composite plates. The effects of plate length–thickness ratio, modulus ratio and stacking sequence on the static bending and free vibration behaviors of laminated plate are also discussed.

Detection of Hermitian connections in wave equations with cubic non-linearity

We consider the geometric non-linear inverse problem of recovering a Hermitian connection A from the source-to-solution map of the cubic wave equation \Box_{A}\phi+\kappa |\phi|^{2}\phi=f , where \kappa\neq 0 and \Box_{A} is the connection wave operator in the Minkowski space \mathbb{R}^{1+3} . The equation arises naturally when considering the Yang–Mills–Higgs equations with Mexican hat type potentials. Our proof exploits the microlocal analysis of non-linear wave interactions, but instead of employing information contained in the geometry of the wave front sets as in previous literature, we study the principal symbols of waves generated by suitable interactions. Moreover, our approach relies on inversion of a novel non-abelian broken light ray transform, a result interesting in its own right.

Geometrical nonlinear problems of truss beam by base force element method

AbstractThe base force element method (BFEM), formulated according the principle of complementary energy, is a new finite element method (FEM) that deals with nonlinear problems. Using the BFEM, the linear elastic model and large elastic deformation model of the plane truss element are derived, and the large elastic deformation model is expanded into a three‐dimensional setting in this study. The rotating part of the element should be considered when deriving the large elastic deformation model. Accordingly, it is necessary to determine whether base force can be used as a fundamental unknown variable. Nonlinear numerical calculation is performed in combination with large elastic deformations of the truss beam and frame. The calculated results conform with the theoretical results of a solid beam with equivalent deflection. In this study, the U.L and T.L formats are used to solve the governing equations iteratively. The calculated results in the T.L format are compared with those of the T2D2 and LINK1 elements in the finite element software. Only a single loading of the T.L format is necessary, rendering it a simple and convenient approach that can improve calculation efficiency. Moreover, the arc‐length method is first applied to the BFEM to solve the snap‐through problem.

High efficiency analysis model for composite honeycomb sandwich plate by using variational asymptotic method

In this article, an equivalent model (called the two-dimensional equivalent plate model (2D-EPM)) of a composite honeycomb sandwich plate (CHSP) is developed using the variational asymptotic method (VAM). The three-dimensional (3D) geometric nonlinear problem of the CHSP is decoupled into a linear constitutive model over a unit cell and a geometric nonlinear problem defined in the 2D-EPM. In the linear constitutive model, the equivalent plate properties are calculated and imported into the 2D-EPM to carry out static, buckling, and vibration analysis. The effects of the layup configurations of the face sheet, geometric parameters of the honeycomb core, and boundary conditions on the equivalent stiffness and the static, buckling, and free-vibration responses are systematically studied. Compared with the 3D finite element method and 3D traditional equivalent model, the 2D-EPM possesses the merits of high precision and calculation efficiency. The equivalent stiffness and anisotropy of the CHSP are very sensitive to the layup configuration as well as the side length and cell corrugation angle of the honeycomb core. The present model can accurately capture the local field distribution within the unit cell as well as provides an effective method for the design and optimization of the CHSP.

Static and dynamic analysis of Isogrid Stiffened Composite Plates (ISCP) using equivalent model based on variational asymptotic method

The isogrid stiffened composite plate (ISCP) can be used to resist bending and buckling loads while being lightweight. In order to reveal the relationship between structural parameters and static/dynamic behavior, the original geometrical nonlinear problem of ISCP is decoupled into a linear constitutive modeling over the unit cell and a geometrically nonlinear analysis over the two-dimensional equivalent plate model (2D-EPM). The equivalent stiffness, static deformation, natural vibration frequencies and buckling mode of ISCP under different layup configurations and structural parameters are calculated based on 2D-EPM, and verified by comparing with the results of three-dimensional finite element (3D-FEM). The results show that the equivalent stiffness, buckling load and natural frequency of ISCP increase with the increase of stiffener thickness and height, while decrease with the increase of stiffener spacing due to the special structural form. Compared with the orthogonal stiffened composite plate and honeycomb stiffened composite plate, the bending stiffness and buckling load of ISCP are greater. More importantly, the model can effectively improve the calculation efficiency under the premise of ensuring sufficient accuracy, which is very important for the preliminary design of ISCP.

Analytical Method for Geometric Nonlinear Problems Based on Offshore Derricks

The marine derrick sometimes operates under extreme weather conditions, especially wind; therefore, the buckling analysis of the components in the derrick is one of the critical contents of engineering safety research. This paper aimed to study the local stability of marine derrick and propose an analytical method for geometrically nonlinear problems. The rod in the derrick is simplified as a compression rod with simply supported ends, which is subjected to transverse uniform load. Considering the second-order effect, the differential equations were used to establish the deflection, rotation angle, and bending moment equations of the derrick rod under the lateral uniform load. This method was defined as a geometrically nonlinear analytical method. Moreover, the deflection deformation and stability of the derrick members were analyzed, and the practical calculation formula was obtained. The Ansys analysis results were compared with the calculation results in this paper.

Global buckling analysis of composite honeycomb sandwich plate with negative Poisson’s ratio (CHSP-NPR) using variational asymptotic equivalent model

In present work, the variational asymptotic method is extended to study the bucking of composite honeycomb sandwich plate with negative Poisson’s ratio (CHSP-NPR), which is easily buckle under compressive loads or bending moments and may lead to catastrophic failure. For global bucking with small local rotations, the 3D geometrical nonlinear problem is decoupled into linear constitutive modeling using unit cell and geometrical nonlinear problem defined over the 2D equivalent plate model (2D-EPM). Results using 2D-EPM in global buckling analysis are compared with 3D-FEM results to evaluate the accuracy and efficiency of the present model, and parametric studies are carried out to reveal the relative influence of selective parameters on buckling behavior of CHSP-NPR. The results show the increase of the proportion of honeycomb core and the decrease of fiber volume fraction of face sheet may increase the negative Poisson’s ratio and weaken the buckling resistance of CHSP-NPR, but the buckling loads of CHSP-NPR are larger than those of conventional honeycomb sandwich plate under the same conditions.

A six-node prismatic solid finite element for geometric nonlinear problems in elasticity

The present work deals with an extended six-node prismatic 3D solid finite element to the analysis of nonlinear geometrical problems. The kinematic formulation is based on a virtual Space Fiber Rotation (SFR) concept which conducts to improve the displacement fields with additional displacement terms, presenting rotational degrees of freedom (DOFs). Once the standard and patch tests for linear validation are previously achieved, the present element is assessed again for large displacement and moderate rotation. For this purpose, the total Lagrangian approach is used and the Green–Lagrange strain/Piola–Kirchhoff​ stress tensors are considered. The material behavior considered in this work is restricted to Saint-Venant–Kirchhoff model for 3D large displacements elasticity To demonstrate the efficiency and accuracy of the developed finite element model, extensive and standard nonlinear benchmarks are presented. The obtained results show a good convergence and accuracy compared to similar finite elements and consequently well capability of the present element to deal with geometric nonlinear problems, including prediction of several limit points.

A new geometrically nonlinear topology optimization formulation for controlling maximum displacement

This article presents a novel formulation for geometric nonlinear topology optimization problems. In practical engineering, maximum deflection is frequently used to quantify the stiffness of continuum structures, yet not applied generally as the optimization constraint in geometrically nonlinear topology optimization problems. In this study, the maximum nodal displacement is formulated as a sole constraint. The p-mean aggregation function is adopted to efficiently treat a mass of local displacement constraints imposed on nodes in the user-specified region. The sensitivities of the objective and constraint functions with respect to relative densities are derived. The effect of the aggregate parameter on the final design is further investigated through numerical examples. By comparison with final designs from the traditional formulation, i.e. minimization end compliance with the volume fraction constraint, or minimization of total volume subject to multiple nodal displacement constraints, the optimized results clearly demonstrate the necessity for and efficiency of the present approach.

Preliminary study on flutter scaling of high-aspect ratio wings

As a result of the increasing demand for aircraft performance, the high-aspect-ratio wing (HARW) becomes the primary structural type of the emerging aircraft as it improves the lift-to-drag ratio. However, HARWs result in higher deflections, leading to a geometrical nonlinear behavior and nonlinear aeroelastic problems. In this work, the preliminary study on aeroelastic behavior of two classic types of HARWs, namely, Goland wing and High Altitude Long Endurance (HALE) wing, are investigated. Aeroelastically scaled models using two scaling methods, called classic scaling method and modified scaling method, are applied and compared with each other. Froude number is considered in the modified scaling method. Both static aeroelastic and flutter analyses are conducted on each scaled model by using different scaling methods. The results show that the Froude number is important to the HALE wing, where both static deflects and flutter velocity obtained by the scaled model agree well with the full model when the Froude number similarity is met. Thus, the Froude number may be the key similar parameter for the HALE wing scaling model design. For the Goland wing scaling model, the Froude number could be ignored.

Investigation of geometric nonlinear stability of sandwich functionally graded (SFGM) spherical shells under uniform external pressure using an analytical approach

The geometric nonlinearresponse of spherical shells made of sandwich functionally graded material (SFGM) under uniform external pressure incorporating the effects of transverse shear deformations is considered. The equilibrium and compatibility nonlinear differential equations can be solved by using the modified interaction method. All of the equations are developed based on the first-order shear deformation theory (FSDT). In the present study, the geometric nonlinear problem has been solved for special boundary conditions including movable and fixed clamped supports in the meridional direction. A closed-form nonlinear load-deflection relationship is developed for SFGM shell which expresses the equilibrium path of the shell.

A study of dynamic response of a wind turbine blade based on the multi-body dynamics method

The geometric nonlinear problem caused by large deformation and the aeroelastic issue under extreme wind conditions are becoming more and more prominent, as the flexibility of wind turbine blades enhances. To solve this problem, a model of Blade analysis with Multi-Body (BaMB) method is built by the rigid multi-body dynamics method in absolute coordinates. The model describes geometric nonlinearity and complex geometry of blades, and accurate results can be obtained by the model after blades are reasonably divided. Based on this model, the geometric nonlinearity of a 100 kW blade under static loading and the aeroelastic response under extreme operating gust (EOG) condition are investigated numerically and compared with experimental results. The results show that BaMB model is able to predict more accurate deformation than beam models under static loading when the deformation of the blade increases, especially when the blade is loaded with more than 120% of the maximum design load and the tip deflection is larger than 15.36% of the blade spans. At 210% of the maximum design load, the BaMB model can predict the deformation at the accuracy of 1.48% with respect to the test; however, the accuracies of the Euler-Bernoulli beam and the Timoshenko beam are 18.3% and 16.79%, respectively. Even in the case of large deformation, the BaMB model can reach the accuracy close to the finite element method (FEM) with high computational efficiency. The aeroelastic response of the blade under EOG condition is analyzed, and the results show that the BaMB model predicts reliable aeroelastic characteristics of the blade compared with commercial software.

Dynamic stability and nonlinear transient behaviors of CNT-reinforced fiber/polymer composite cylindrical panels with delamination around a cutout

This study dealt with the dynamic stability and geometrical nonlinear problems of carbon nanotube/fiber/polymer composite (CNTFPC) cylindrical panels without or with delamination around a central cutout. A multiscale analysis using the Hewitt and Malherbe model was performed to determine the carbon nanotube (CNT) weight ratios, thickness–radius ratios, thickness–length ratios, and delamination area ratios around a cutout. A delamination around a central cutout was modeled in two dimensions by introducing continuity conditions of displacements at the delamination boundaries. The proposed approach in this study has been verified by previous studies. Parametric results showed the significance of a proper CNT ratio and curvature for better structural performance on the dynamic instability and nonlinearity of delaminated CNTFPC cylindrical panels.

Base functions effect in stability finite element analysis of compressed plate

Geometric nonlinear solution of a compressed plate is presented in this paper. Basic assumptions are specified and incremental conditional equations are derived from the variational principle of minimum of total potential energy. Full Newton-Raphson procedure, in which the stiffness matrix is updated at every equilibrium iteration, has been applied for solution. The importance of modifications of base functions for solving geometric nonlinear problems is analysed. The solved example is presented, the differences are compared and explained.

Theoretical and Experimental Free Vibration Analysis of a Loaded Curved Beam With Moving Boundaries

The present article theoretically and experimentally investigates free vibration characteristics of generalized curved beams with moving boundaries. The dynamic behavior is characterized about deformed configuration, attained under different concentrated loads, and rigidly connected to the midpoint of the beam. The coupled static and dynamic analysis of the geometric nonlinear problem is decomposed into two parts: the static problem dealing with large deformed configuration and the dynamic problem dealing with small amplitude free vibration of the deformed configuration beam. The analysis is carried out incrementally in embedded curvilinear coordinate frames using variational principle. The governing equation of the static problem is derived for a combined effect of bending and center line extension. The governing equation for free vibration is derived at the particular configuration of the updated beam geometry, using Hamilton's principle. The comparison between the numerical and experimental results successfully validates the proposed semi-analytical model and leads toward some meaningful observations.