Geometric Nonlinear Effects Research Articles

Large Deformation Behavior of Plane Periodic Truss Networks. Part 1. Closed-Form Solution for Single Node Cells

This article focuses on the derivation of explicit descriptions of networks in large deformation through the homogenization method of discrete media. Analytical models are established for the in-plane behavior of a planar periodic truss, whose cell contains a single node, as frequently encountered in practice. The cell is composed of bars that support only axial forces and are connected by perfect hinges. For the considered type of trusses, (given that the equilibrium conditions of the node and of the cell coincide) closed-form expressions for the local behaviour in the case of large deformations can be derived. This case makes it possible to combine the non-linearities arising from large deformations on the one hand and rheological characteristics on the other, and to compare their respective effects as a function of cell morphology. The results are illustrated by the shear and extension responses of specific trusses. The analysis is carried out for bars with stiffening, linear or softening behavior. The combination of the effects of geometrical non-linearities, rheological non-linearities and anisotropy results in particularly rich behaviors of the network.

Effects of aeroelastic coupling accuracy and geometrical nonlinearity on performances of optimized composite wings

Effects of aeroelastic coupling accuracy and geometrical nonlinearity on performances of optimized composite wings

The Effect of a Fully Asymmetric Discontinuity in the Elastic Layer of a Geometrically Nonlinear Double-Beam Coupled Mechanical System

This paper presents the effect of an antisymmetric discontinuity in a Winkler nonlinear elastic layer and compares it with the case of a double Timoshenko beam system without discontinuities. The effects of geometric nonlinearity are considered, and the obtained results represent a time-domain analysis. A modified p-version finite element method is applied to analyse the vibrations of mechanical systems with discontinuities. The main contribution of this work is a comparative analysis of a double beam system without discontinuities and a double beam system with an antisymmetric discontinuity in the Winkler elastic layer. The study demonstrates significant deviations in the beam response under a concentrated periodic external force when an antisymmetric discontinuity is present. Its qualitative and quantitative characteristics are illustrated through time histories, showing amplitude variations in the steady-state oscillation regime. Forced vibrations in the time domain are analysed using the Newmark direct integration method. The cases of deviations in the antisymmetric model are explained, highlighting their potential applications in technical practice as well as in the field of deformable bodies and structures.

Optimized Design and Test of Geometrically Nonlinear Static Aeroelasticity Model for High-Speed High-Aspect-Ratio Wing

Large transport aircraft tend to adopt a wing layout with a high aspect ratio and swept-back angle due to the requirement of a high lift-to-drag ratio. Composite material is typically employed to ensure the light weight of the structure, causing serious static aeroelasticity problems to the aircraft. When the airplane is flying in the transonic region, its aerodynamic load is very complex, and the large load leads to large deformation of the wing, triggering geometric nonlinear effects, which further affects the static aerodynamic elasticity characteristics of the wing. In this study, in order to study the static aeroelastic characteristics of the transonic flow of a high-aspect-ratio airfoil, a new design method of the scaled similar optimization model is described, and the change in the model lift coefficient due to geometrically nonlinear static aeroelasticity effects when the angle of attack is changed was investigated by using simulation and wind tunnel test methods. In order to ensure the accuracy of the wing shape when the model was deformed greatly, this study employed the structural design scheme of the wing with the skin as the main stiffness component, and the thicknesses of different regions of the skin were used as the design variables for the stiffness optimization design. The engineering algorithm of nonlinear finite elements was used in this study to calculate the curve of lift with the angle of attack considering the geometric nonlinear static aeroelasticity effect. The results show that the similarity optimization process employed in this study can be used to complete the design of the high-speed aerostatic wing test model, and the wind tunnel test results show that geometric nonlinearity has a large impact on the lift coefficient of the wing.

Stability Analysis of Curved Beams Based on First-Order Shear Deformation Theory and Moving Least-Squares Approximation

Based on the first-order shear deformation theory (FSDT) and moving least-squares approximation (MLS), a new meshfree method that considers the effects of geometric nonlinearity and the pre- and post-buckling behaviors of curved beams is proposed. An incremental equilibrium equation is established with the Updated Lagrangian (UL) formulation under the von Karman deflection theory. The proposed method is applied to several numerical examples, and the results are compared with those from previous studies to demonstrate its convergence and accuracy. The pre- and post-buckling behaviors of the curved beam with different parameters, such as vector span ratios, bending forms, inclusion angles, boundary conditions, slenderness ratios, and axial shear stiffness ratios, are also investigated. The effects of the parameters on the buckling response are demonstrated. The proposed method can be extended to the study of double nonlinearities of curved beams in the future. This extension will provide a more scientific reference basis for the structural selection of curved girder structures in practical engineering.

Assessment of Building Nondeterministic Dynamic Structural Behavior considering the Effect of Geometric Nonlinearity and Aerodynamic Damping

The objective of this research is to evaluate the dynamic structural response of tall buildings subjected to wind loads, taking into account the influence of geometric nonlinearity and aerodynamic damping. The project focuses on a steel-concrete composite structure with 48 floors and a height of 172.8 m, examining its response to wind non-deterministic dynamic actions. The building finite element model was developed based on the Finite Element Method (FEM), using the ANSYS computational program, and considering the soil-structure interaction effect, with the objective of obtaining a realistic representation of the dynamic behavior. The building dynamic response was obtained based on the displacement and acceleration values, determined with the consideration of a wind velocity range between 5 m/s (18 km/h) and 45 m/s (162 km/h). The findings of this study indicate that when the effect of geometric nonlinearity was incorporated into the analysis, the dynamic response of the investigated building exhibited notable discrepancies. The maximum differences observed in the horizontal translational displacements and accelerations were 30% and 45%, respectively. In contrast, the inclusion of aerodynamic damping had a negligible impact on the structural dynamic response, with maximum differences of 5% for displacements and 10% for accelerations.

Assessment of the Tall Buildings Dynamic Response Considering the Geometric Nonlinearity and the Aerodynamic Damping

This research work aims to evaluate the dynamic structural behaviour of tall buildings when subjected to wind loads considering the effect of the geometric nonlinearity and also the aerodynamic damping, due to the relative movement between the structure and the wind action. This way, the project associated to a steel-concrete composite building with 48 floors and 172.8 m height is investigated, when subjected to wind nondeterministic dynamic actions. The composite building finite element model was developed based on the use of the Finite Element Method (FEM), utilising the ANSYS computational program, and considering the soil-structure interaction effect, aiming to obtain a realistic representation of the dynamic behaviour. The building dynamic response was obtained based on the displacements and accelerations values, determined having in mind a wind velocity range between 5 m/s [18 km/h] and 45 m/s [162 km/h]. The conclusions of this investigation pointed out to the fact that when the geometric nonlinearity effect was considered in the analysis the investigated building dynamic response presented relevant differences, with maximum differences up to 30% to horizontal translational displacements and up to 45% to accelerations. On the other hand, when the aerodynamic damping was considered the contribution was not significant to the structure dynamic response, with maximum differences up to 5% for the displacements and up to 10% for the accelerations.

UHPFRC structural analysis from a geometrically exact Extended Lumped Damage Mechanics approach

The use of ultra-high-performance fibre-reinforced concrete (UHPFRC) has significantly increased in the recent years. However, the accurate mechanical behaviour modelling of this complex material is still a challenge in the present. Because the materials high load-bearing capacity and the presence of fibbers, this type of problem experiments large displacements before the failure. In this study, the material damage description has been performed by the Extended Lumped Damage Mechanics. Additionally, an approach based on the nodal positions of the Finite Element Method has been utilised, which makes the formulation geometrically exact. Thus, this study evaluates the failure of structures composed of UHPFRC, accounting for the effects of material and geometric nonlinearities computed by the Extended Lumped Damage Mechanics and the Finite Element Method based on positions, respectively.

Third-order geometric stiffness formulation for improved mesh convergence of thin and wide spatial beams in the generalized strain beam formulation

AbstractThis paper presents the stiffness formulation of a beam element with the relevant third-order nonlinear geometric effects for relatively wide and thin rectangular beams, in particular when loaded in the plane and simultaneously deformed out of the plane. The element is initially straight in its undeformed configuration. The formulation is based on Timoshenko beam theory with nonuniform torsion and Wagner effects. The derivation is carried out by means of the Hellinger–Reissner variational principle with custom interpolation functions. The element is incorporated into the generalized strain beam formulation for multibody systems. Numerical simulations of precision flexure mechanisms show that the use of a single third-order element per flexible member can already yield adequate performance, at a significant reduction of the necessary degrees of freedom and the computation time, compared with using multiple second-order elements in the generalized strain beam formulation.

Biaxial bending strength of thin silicon dies in the ring-on-ring test by considering geometric nonlinearity and material anisotropy

The ring-on-ring test (RoR) is a standard biaxial bending test specified in ASTM C1499-19 and ISO 17167. This test has been utilized for characterizing the biaxial bending strength of silicon dies or wafers to eliminate the die edge chipping effect in the four-point bending test. However, judging from the literature, when testing thin silicon dies, the test is subject to geometric nonlinear effects. This study aims to investigate this nonlinear mechanics in the RoR test using experimental, theoretical, and numerical methods while considering silicon material anisotropy. A 2D-isotropy model of a nonlinear finite element method (NFEM) simulation with specimen elastic modulus of 130 GPa is utilized and verified by experiments and a 3D-anisotropy model in terms of deformation (or displacement) and stresses. Based on the 2D-isotropy NFEM solutions, the fitting equations of correction factors to the theoretical solution are proposed and implemented on determining the biaxial bending strength of 10 mm × 10 mm silicon dies ranging from 57 μm to 297 μm in thickness. It is found that those proposed fitting equations are independent on the test specimen thickness, radius, and materials but not on the radii of the loading and supporting rings. It has also been successfully demonstrated that the RoR test using the theory associated with the correction factor equations can be easy to use to determine the biaxial bending strength of the thin silicon dies that frequently failed in the nonlinear range.

Wave Propagation in Prestressed Structures with Geometric Nonlinearities Through Carrera Unified Formulation

This paper deals with the analysis of wave propagation characteristics in various prestressed structures with geometric nonlinearities using the Carrera Unified Formulation (CUF). CUF provides a versatile platform to model a wide range of structures and nonlinearities that can take care of all wave propagation aspects. In this work, different geometric nonlinearities for which representative governing equations have been derived and numerical solutions have been obtained through a unified approach are considered. The study investigates in detail the effect of prestress and geometric nonlinearity on wave propagation behavior. The results indicate that prestress has a very influential effect on modal frequency and dispersion characteristics for wave propagation. Specifically, three CUF-modeled beams are considered herein, having a sandwich, metallic portal, and metallic box cross section, respectively. Initially, the principal cross-sectional modal shapes of the unstressed, linear, and full nonlinear (i.e., full three-dimensional Green–Lagrange strain matrix) beam with a prestress are investigated, among which torsional and flexural modes can be recognized. Afterward, the equilibrium curves of such structures for various geometrical nonlinear approximations are traced, highlighting that most types of nonlinearity induce a hardening behavior in the system, which increases with the preload, directly leading to a variation in modal frequencies. The dispersion relations of the full nonlinear structure examined as a function of the applied preload are further compared, enriching the investigation by exploiting wave finite element method capabilities. This knowledge paves the way toward the design and optimization of prestressed systems with enhanced acoustic performance, and that fosters the development of sound absorption, noise insulation, and structural isolation.

Nonlinear analysis of three-dimensional hyperelastic problems using radial point interpolation method

Hyperelastic materials are primarily common in real life as well as in industry applications, and studying this kind of material is still an active research area. Naturally, the characteristic of hyperelastic material will be expressed when it undergoes large deformation, so the geometrical nonlinear effect should be considered. To analyze the behavior of hyperelastic material, the Neo-Hookean model is imposed in this study because of its simplicity. The model shows the nonlinear behavior when the deformation becomes large due to the nonlinear displacement-strain relation. This constitutive relation also gives a good correlation with experimental data. This study performs a meshless method, namely the radial point interpolation method (RPIM), to analyze the nonlinear behavior of Neo-Hookean hyperelastic material under a finite deformation state in three-dimensional space. The standard Newton-Raphson technique is applied to obtain the nonlinear solutions. Unlike mesh-based approaches, the meshless method shows its advantages in large deformation problems due to its mesh independence. In this paper, the numerical results of three-dimensional problems that undergo large deformation will be calculated and validated with solutions derived from previous studies. By investigating the obtained results, the superior ability of RPIM in hyperelastic problems can be proved.

A fast search method of buckling load for telescopic boom structure

The telescopic boom structures are extensively utilized in engineering applications involving large mobile cranes, aerial work platforms of significant height, and similar mechanical devices. These are predominantly fabricated using solid-webbed box types, latticed truss designs, or a combination thereof. Under load, they exhibit pronounced geometric nonlinear effects, with the relationship between load and displacement demonstrating marked nonlinear characteristics. This paper focuses on the geometric nonlinear modeling of slender multi flexible beam structures. The overall structural system is divided into several substructures, and the concept of multi flexible system modeling is borrowed to establish a follow-up connected body foundation on each substructure. By decomposing the node displacement and rotation in the substructure, the large displacement and large rotation of the node are decomposed into rigid body motion of the connected base and small displacement and small rotation relative to the connected base, effectively representing the large displacement and large rotation of the substructure as rigid body motion of the connected base. A modeling method for the geometric nonlinear analysis of slender and flexible multibody beam structures is proposed. By decomposing the nodal displacement and rotation within the substructures, the large displacement and rotation of the nodes are broken down into the rigid body motion of the body-fixed coordinate and small displacement and rotation relative to the body-fixed coordinate. This approach establishes the application conditions for calculating the structure’s virtual power of deformation using traditional beam elements with linear strain. A method for solving the instability load of slender and flexible multibody structures is proposed. This method integrates the characteristics of the system’s nonlinear equilibrium equations with respect to load, by deriving the system equations with respect to a load increment control parameter. This paper converts nonlinear equilibrium equations into first-order ordinary differential equation (ODE). The method proposed in this paper provides a more efficient solution for the buckling load of the telescopic boom. It can be used to systematically and quickly calculate the structure of the telescopic boom.

Dynamic Modelling and Performance Analysis of Deployable Telescopic Tubular Mast

AbstractThis work presents the longitudinal and transverse coupling vibrations of a deployable Telescopic Tubular Mast (TTM), a multi-stepped structure integrated into a spacecraft system, while considering the rigid-flexible coupling phenomenon. The model is derived using the principle of virtual work and discretized via the variable separation method. The von Kármán strain is employed to incorporate geometric nonlinear effects. Semi-analytical results for the shape functions and natural frequencies of the quasi-static multi-stepped boom are obtained using the extended transfer matrix method (ETMM). These natural frequencies are validated against results from Nastran, confirming the ETMM's accuracy. In addition, the model accounts for the continuously changing natural frequencies and shape functions during the deployment phase. Finally, the dynamic phenomena of the longitudinal and transverse displacements are analyzed at various deploying states, including locking and restart behaviors. The influence of the structural damping on the vibration evolution is also contained in the numerical analysis.

Systematic Experimental Evaluation of Aeroelastic Characteristics of a Highly Flexible Wing Demonstrator

This paper presents a comprehensive experimental analysis of the evolutionary modal characteristics of a highly flexible wing that exhibits bending–torsion coupling-driven instability. By implementing operational modal analysis on responses triggered by a combination of an external pulse-like stimulation and turbulence within the flow, this paper presents the airspeed-driven variations of the modal frequencies, damping ratios, and the underlying modal coupling behavior, leading to instability. This analysis is extended to varying the wing root pitch angles through which the effects of geometrical nonlinearity are exercised. Their effects are particularly noted on the hump feature of the airspeed-driven damping ratio locus of the mode responsible for instability. The decreasing critical damping ratio is shown to result in amplified turbulence-driven responses, which pose significant challenges to identification procedures by masking the visibility of other modes. Furthermore, through a novel technique used to analyze the modal coupling, the relative phase and magnitude properties of the coupled bending–torsion composition of the critical mode before and at flutter onset are evidenced experimentally. It is demonstrated that these relative participation measures provide a strong indication of the response content of the limit cycle oscillations that emerge after the flutter speed.

Finite Element Modeling and Calibration of a Three-Span Continuous Suspension Bridge Based on Loop Adjustment and Temperature Correction.

Precise finite element modeling is critically important for the construction and maintenance of long-span suspension bridges. During the process of modeling, shape-finding and model calibration directly impact the accuracy and reliability. Scholars have provided numerous alternative proposals for the shape-finding of main cables in suspension bridges from both theoretical and finite element analysis perspectives. However, it is difficult to apply these solutions to suspension bridges with special components. Seeking a viable solution for such suspension bridges holds practical significance. The Nanjing Qixiashan Yangtze River Bridge is the first three-span suspension bridge in China. To maintain the configuration of the main cable, the suspension bridge is equipped with specialized suspenders near the anchors, referred to as displacement-limiting suspenders. It is the first suspension bridge in China to use displacement-limiting suspenders and their anchorage system. Taking the suspension bridge as a research background, this paper introduces a refined finite element modeling approach considering the effect of geometric nonlinearity. Firstly, based on the loop adjustment and temperature correction, the shape-finding and force assessment of the main cables are carried out. On this basis, a nonlinear finite element model of the bridge was established and calibrated, taking into account factors such as pylon settlement and cable saddle precession. Finally, the static and dynamic characteristics of the suspension bridge were thoroughly investigated. This study aims to provide a reference for the design, construction and operation of the three-span continuous suspension bridge.

Nonlinear thermo-electro-mechanical responses and active control of functionally graded piezoelectric plates subjected to strong electric fields

Functionally graded piezoelectric plates (FGPPs) are often exposed to extreme thermal environments and subjected to large amplitude excitation and strong electric fields. Accurately predicting the nonlinear behaviors of FGPPs under large thermo-electro-mechanical loads remains a considerable challenge. This paper proposes a comprehensive nonlinear coupled analysis model that considers geometric nonlinearity, piezoelectric nonlinearity, and the temperature dependence of piezoelectric parameters. The total Lagrangian incremental finite element equations for FGPPs under thermo-electro-mechanical loads are derived using Hamilton's principle, by employing the first-order shear deformation theory and the von Kármán nonlinear strain-displacement relationship. The accuracy of the model is validated through comparative studies. Based on this multi-nonlinear model, we further investigate the effects of geometric nonlinearity, piezoelectric nonlinearity, and temperature dependence on the nonlinear static bending, dynamic responses, and active control of FGPPs. This study demonstrates that considering these factors enables accurate prediction of the static, dynamic, and active control behaviors of FGPPs.

Simultaneous effects of material and geometric nonlinearities on nonlinear vibration of nanobeam with surface energy effects

Simultaneous effects of material and geometric nonlinearities on nonlinear vibration of nanobeam with surface energy effects

Fracture modeling of curved composite shell structures using augmented finite element method

This paper presents an augmented finite element method for the fracture modeling of curved composite shell structures considering geometric nonlinear effects. We first derive the composite shell AFEM (CS-AFEM) formulation using a dynamic implicit algorithm, which enhances the numerical convergence when dealing with unstable crack propagations. Besides, the cohesive zone model featuring with shell kinematics is incorporated into the CS-AFEM to describe the quasi-brittle fracture behaviors of composite laminates. Furthermore, a coordinate transformation scheme is proposed to describe both the local material orientation and the crack evolving path in the curved shell structures. Finally, several benchmark examples are numerically investigated, and the capability of the proposed method in modeling the arbitrary evolving cracks in curved composite shell structures has been thoroughly demonstrated.

Feasible model-order reduction approach for analysis of composite rotor blades based on geometrically exact beam formulation

This paper presents a novel and practical reduced-order model (ROM) approach designed specifically for analyzing composite rotor blades, leveraging the geometrically exact beam formulation. The slender nature of rotor blades necessitates aero-structure coupled analysis to precisely predict their response, which involved numerous iterative computations. By capturing large displacements and rotations, this approach enhances the accuracy of blade behavior predictions under operational conditions. To address the computational demands of large-scale analyses, a ROM technique that effectively reduces system dimensionality while preserving critical structural features is introduced. The proposed method is then applied to the aero-structure interaction analysis of a hingeless hovering rotor trim, incorporating geometrical nonlinearity and centrifugal effects. The analysis results demonstrate that the ROM accurately captures the dynamics of these complex aeroelastic systems while significantly reducing computational costs. This approach exhibits significant potential for various aerospace applications, particularly in the design and analysis of structures undergoing geometrical nonlinear behavior and rotation-induced loads.