Geometric Nonlinear Effects Research Articles

A nonlinear geometric model for pre-stressed steel–concrete composite beams

Steel–concrete composite beams are commonly employed in civil constructions such as multi-storey building floors and long-span bridges. In case of significant span to depth ratios, excessive deflections and noticeable crack widths at the concrete slab may occur at the serviceability stage. In this context, internal or external pre-stressed tendons can be used as a remediation. In the latter case, significant effects of geometric non-linearity may arise due to the strain incompatibility between the external tendon and the composite member, resulting in a variable tendon eccentricity during deformation. In this paper, second-order effects are evaluated in eight pre-stressed steel–concrete composite beams for which experimental results are available. Hence, a three-dimensional finite element model using a Lagrangian description is proposed. The external tendons are represented by one-dimensional catenary elements, whereas the reinforced concrete slab and steel profile are modeled by shells finite elements. Slipping at the slab-beam interface and tendon-deviator locations are also included in the analysis. For the studied externally pre-stressed beams, the introduction of nonlinear geometric behavior yields lower collapses loads in relation to its linear counterpart, varying this difference between 6.4 and 9.1%.

Distortion and losses of sonic booms through turbulent fields

Distortion and losses due to scattering of sonic booms propagating through turbulent fields are investigated using an extended Burgers equation that incorporates an extinction coefficient model previously reported by the author. The extinction coefficient, induced by turbulence, is modeled as a correction to the free field wavenumber using multiple scattering theory. It is a complex-valued function whose real part leads to a frequency dependent attenuation while the imaginary part results in additional dispersion of sonic booms. Numerical calculation of the extinction coefficient is validated using an exact solution derived for a turbulent field with an exponentially decaying correlation function. The model is suitable for direct integration into any Burgers equation that only accounts for geometrical spreading, nonlinear, and atmospheric absorption effects. The extended Burgers equation lends itself to a very efficient algorithm compared to other sonic boom numerical models developed to account for turbulent fields. The algorithm is then used to model sonic boom waveform distortion and loudness variability through randomly generated, realistic turbulent fields. The effects of the intensity and correlation length of the turbulence on the loudness of N-waves and shaped booms are examined and will be presented.

Vibro-acoustics of Central Africa harps

Central Africa harps are string instruments, often anthropomorphic, whose soundbox is built from a hollowed out tree trunk. There strings, usually 8 in number using nowadays fishing line, are wrapped to wooden tuning pegs on the neck and attached to a tailpiece placed under animal skin used as soundboard. Each instrument-making element can vary according to ethnic groups and material availability. This study aims at understanding the vibro-acoustic behavior of these instruments in order to determine relevant acoustic descriptors linked to there building process. Hence, a numerical model is developed based on the Udwadia-Kalaba modal formulation, relying on substructuring concepts. Each subsystem's dynamics is described by its modal parameters in terms of unconstrained modes and the coupling is enforced by boundary conditions. Strings displacement is described in two polarizations including geometrical nonlinear effects. Modal parameters are experimentally identified, on severa harps collected from different ethnic groups, and turn out to be discriminating descriptors. The reliability of the model is validated against laboratory measurements. Finally, sound syntheses based on the proposed approach are compared to experimental data, showing good agreement. [This work, part of the project NGombi, was funded by the Agence Nationale de la Recherche (French National research agency), Grant No. ANR-19-CE27-0013-01.]

Quasi-Steady Aeroelastic Analysis of the Semi-Aeroelastic Hinge Including Geometric Nonlinearities

A recent consideration in aircraft design is the use of folding wingtips, with the aim of enabling higher-aspect-ratio wings with less induced drag but also meeting airport gate limitations. A formulation is introduced to account for finite rotations of rigid folding wingtips attached through hinges on a flexible airframe structure including also aerodynamic follower forces for the folding wingtip components. This study investigates the effects of geometric nonlinearities on the quasi-steady aeroelastic response of floating wingtips. It is found that the wingtip response can vary significantly when geometric nonlinearities are accounted for; however, a small impact was observed on the main airframe structure.

Effects of shear deformation and orthotropy on the buckling behaviour of oriented strand boards

ABSTRACT The literature is replete with studies conducted on wood-based boards. However, studies involving the influence of orthotropy and shear deformation on the one-dimensional buckling behaviour of oriented strand boards are lacking. This study is a step-by-step approach towards investigating and discussing the influence of orthotropy and shear deformation on the bending and one-dimensional buckling behaviour of oriented strand boards using specimens which are 12, 18, and 25 mm in thickness, measuring 400 and 780 mm in length for the bending analyses and 400, 425, 450, 475, and 500 mm for the buckling analyses. FE-models were developed which considered the boards as orthotropic and were able to determine their load-displacement behaviour considering the effects of geometric non-linearities. Results of the analyses showed that orthotropy have significant effects on the bending while shear deformation influences both the bending and buckling behaviour of oriented strand boards. In bending, the effects are generally higher in the main strength than in the secondary strength direction. In buckling, it is a reduction in the buckling loads in a range of between 4% and 26%, compared to what would have been obtained using the Euler equation. An alternative Equation with a better ability to predict the one-dimensional buckling load of wood-based boards was presented and discussed.

Numerical analysis of geometrical nonlinear aeroelasticity with CFD/CSD method

Abstract A nonlinear static aeroelastic methodology based on the coupled CFD/CSD approach has been developed to study the geometrical nonlinear aeroelastic behaviors of high-aspect-ratio or multi-material flexible aerial vehicles under aerodynamic loads. The Reynolds-averaged Navier–Stokes solver combined with the three-dimensional finite-element nonlinear solver is used to perform the fluid-structure coupling simulation. The interpolation technique for data transfer between the aerodynamic and structural modules employs radial basis function algorithm as well as dynamic mesh deformation. A high-aspect-ratio structure with multi-material is modeled by the finite element method to investigate the effects of geometrical nonlinearity on the aeroelastic behavior. Numerical simulations of the linear and nonlinear static aeroelasticity were conducted at transonic regime with different angles of attack. By comparing the aeroelastic behaviors of linear and nonlinear structure, it shows that geometrical nonlinearity plays an important role for flexible high-aspect-ratio wings undergoing the large static aeroelastic deformation and should be taken into account in aeroelastic analysis for such structures.

The Effect of Nonlinear Behavior of Bolted Connections on Dynamic Analysis of Steel Transmission Towers

Transmission towers are kinds of complex lattice structures which affects their accurate modeling and analysis and brings about some problems in the prediction of their actual behavior. For this reason, full-scale experiments are usually applied for transmission towers to examine their resistance and control their behavior. In this paper, the displacements of a transmission tower in the full-scale test, including effective parameters such as geometric and material nonlinearity and joint slip effect are attained applying the developed nonlinear analysis software. These displacements for four cases of analysis: linear, geometric nonlinear, geometric and material nonlinear and lastly, geometric and material nonlinear along with joint slip effect are obtained and compared with the results of the full-scale test. In this comparison, the results of geometric and material nonlinear analysis along with joint slip effect coincide well with the results of the full-scale experiment which demonstrates the joint slip effect importance and the capability of developed software. Finally, the tower natural frequencies are obtained and it is obvious that taking the joint slip effect into account of the analysis reduces the natural frequencies of the tower as a significant parameter in the dynamic analysis of these kind of structures either individually or as coupled system along with conductors.

A Study on Prediction of Process Parameters of Shot Peen Forming Using Artificial Neural Network Optimized by Genetic Algorithm

Shot peening is an important process for the forming in aerospace industries. However, it is difficult to design the process parameters because of the complex nonlinear relationship between shot peening parameters and the deformation response of shot peened components which is affected by various nonlinear factors such as geometric nonlinearity, material nonlinearity, and coupling effects between process parameters. In this paper, a back propagation artificial neural network (BP-ANN) optimized by genetic algorithm (GA) method, called GA-ANN, is presented for the prediction of shot peen forming parameters. GA is applied to optimize the initial parameters of the BP-ANN to avoid falling into local minimum error. The initially optimized BP-ANN is then directly used to simulate the complex nonlinear relationships between the shot peening parameters (e.g. air pressure, shot mass flow, workpiece feeding speed, etc.) and the mechanical responses of the workpiece (e.g. the bending radius of target workpiece). The experimental results show that the shot peen forming process parameters can be effectively predicted by BP-ANN and that the prediction accuracy can be significantly improved when the ANN model is optimized first using a GA algorithm.

Nonlinear free vibration analysis of piezoelectric laminated plate with random actuation electric potential difference and thermal loading

Solutions to nonlinear free vibration analysis of an arbitrarily laminated thin rectangular plate subjected to thermo-piezoelectric load is investigated. The governing equation of motion is based on von Kármán’s deflection of thin plates to capture the effects of moderate geometric nonlinearity. Induced strain actuation assumption is confined to a linear model for applied low electric fields and varying temperature distribution along the thickness direction. The solution for lateral displacement field for simply supported and clamped condition edges are determined by displacement-stress; mixed formulation. The applied Galerkin’s projection reduces the governing nonlinear partial differential equation to a time dependent ordinary differential equation. Solutions are obtained using a predictor-corrector numerical integration scheme. The effects of randomly applied actuation potential and thermal loading on nonlinear frequency ratio are examined. The marginal values provided using various probabilistic methods are found to be in good agreement with each other.

Numerical modelling of in-plane restrained concrete two-way slabs subjected to fire

This paper presents a numerical investigation of the fire performance of eight reinforced concrete two-way slabs subjected to different in-plane restraints. A comparison of the experimental results with results predicted by a numerical model showed generally satisfactory agreement. The effects of geometric nonlinearity, or linearity, and concrete thermal strain on the fire behaviour of the tested slabs were analysed. It was found that neglecting the geometric nonlinearity led to lower predicted deflections for in-plane restrained slabs and higher predicted deflections for simply supported slabs, while a larger concrete thermal strain led to larger deflections for the concrete slabs under either restraint condition. Parametric studies were conducted to investigate the influence of in-plane restraint type, restraint level, aspect ratio, reinforcement ratio and layout, and slab thickness on the fire behaviour of the in-plane restrained slabs. The results of the parametric studies showed that the in-plane restraint type, restraint level, and aspect ratio significantly affect the deflection trends, failure mode, and fire resistance of in-plane restrained slabs. In addition, the fire-resistant performance for in-plane restrained rectangular slabs can be improved by increasing the reinforcement ratios along the short span.

Dynamic response of dry cask storage systems for spent nuclear fuel to near field blast loading

Dry storage casks are the most common form of spent nuclear fuel (SNF) storage in the United States. An explosion near a spent nuclear storage facility poses a serious public risk due to the potential of radioactive leakage. In this study, for the first time, the structural performance of vertical steel–concrete-steel sandwich (SCSS) and reinforced concrete (RC) casks under blast loading scenarios is studied using explicit finite element simulations considering material and geometric nonlinearity and strain rate effects. The response of the cask is investigated in terms of stress levels, deformations, and peak accelerations. The conventional weapons (CONWEP) model was used to induce a blast load on the structure at varying blast charges. The accelerations experienced by the canister and the fuel assemblies, which are critical for design are estimated. The inherent vibration damping characteristics of the cask are evaluated, and a novel damper configuration is proposed to improve the energy dissipation capacity of the system. The results showed that the general integrity of the cask could be preserved in the presence of a thick reinforced concrete layer. However, due to the lack of a damping mechanism, the blast wave can propagate through the system and result in very large accelerations in the canister and the fuel assemblies. Results also revealed that the SCSS configuration has a more ductile response compared to the RC design. The results of this study could be used for the safety evaluation and design optimization of current casks in service and other cylindrical composite containment structures.

Nonlinear dynamic response of an L-shaped beam-mass piezoelectric energy harvester

Piezoelectric energy harvesters (PEHs) have been taken considerable attention in decades. To evaluate the performance of the harvester in large deformation and high electric field conditions, nonlinear effects (geometric, material and damping nonlinearities) should be involved in analyzing the characteristic of the harvesters. In this article, the unimorph L-shaped harvester is investigated and influence of the geometric and material nonlinearities to the responses of the proposed L-shaped harvester is also studied. Based on extended Hamilton principle and Gauss law, the distributed parameter model of the L-shaped harvester is established and validated with experiments. Moreover, influence of some key parameters such as excitation amplitude abx and nonlinear material coefficients α1-α4 to the dynamic responses and voltage outputs of the L-shaped harvester are also analyzed. Besides, four different harvesters, which contain linearity only, geometric nonlinearity only, material nonlinearity only and both geometric and material nonlinearities, are investigated to embody the difference and importance of the two nonlinearities (geometric and material nonlinearities). Results show that as the excitation amplitude abx increases, effect of geometric nonlinearity becomes more obvious and leads to the softening phenomenon, and part of nonlinear material coefficients have greater influence to the peak value of the dynamic responses and the nonlinear phenomena (softening or multiple-frequency). Thus, consideration of nonlinear effects (geometric and material nonlinearities) can improve the prediction accuracy of the performance of the harvester which will be helpful for design and application of the harvester in large amplitude excitation and high electric field conditions.

A New Torsion Testing Apparatus for Circular Members

The concrete-filled fiber-reinforced polymer tube (CFFT) is a unique structural element that is well suited for reinforced concrete applications in harsh environments due to the corrosion-resistant reinforcement. It also benefits from the stay-in-place formwork capabilities of the reinforcement and the beneficial concrete confinement offered primarily in cases of axial compression. The strength and response of the CFFT system have been studied under axial, flexural, and combined loading conditions; however, its torsional behavior has not been evaluated. Some of the challenges have been the ability to provide successful gripping of the circular cross-section as well as avoiding the undesired second-order effects when pure torsion is investigated. This paper presents a novel apparatus developed to test circular members, including CFFTs, to failure under a variety of loading conditions including pure torsion, and combined torsion, bending, and axial compression. The apparatus can accommodate a complex set of geometric nonlinearity effects associated with the deformations arising from multiple degrees of freedom. The functionality of the testing system under a state of pure torsion and combined loading was verified. The results showed that the testing apparatus effectively simulated the intended loading condition. The samples experience relatively large and complex displacements that justified the details incorporated in the design of various components of the testing configuration.

Buckling analysis of an innovative type of steel-concrete composite support in tunnels

The steel frame is the main bearing structure that ensures the safety of tunnel construction. Structural damage due to instability is a common occurrence and cannot be ignored. The instability mechanism of the traditional steel arch was analyzed, and an innovative steel frame type called the π-type steel-concrete composite support (π-type SCCS) was proposed to improve the bearing capacity and structural stability. First, the constitutive and interface relations of concrete-filled steel tubes were verified. Then, the buckling model of the π-type SCCS was established by considering the effect of geometric and material nonlinearity. The characteristic parameters of the steel frame were comprehensively analyzed regarding the instability mode, internal force development, and stress variation and were optimized under different construction states. In addition, the influence of different parameters on the structure stability was clarified, including the design of the steel frame and the grouting reinforcement. Finally, the influence of the wall thickness and geometric imperfections on the stability of the π-type SCCS during local buckling was investigated. The results can provide a theoretical basis and references for highly stable tunnel support design

Effects of geometric nonlinearity on the response of a long beam on viscoelastic foundation to a moving mass

We investigate the effect of the nonlinear terms arising from exact geometry on the dynamic response of the mass-beam-foundation system. In particular, we are interested in the case when the moving speed of the point mass exceeds the critical speed. We replace the infinitely long beam with a sufficiently long finite beam and use a harmonic expansion method to discretize the partial differential equation of motion. The feasibility of this technique is verified by comparing our numerical results for the linear stationary case under a point force against existing analytical solutions. By solving the eigenvalues of the linear problem, one can find the linear critical speed for a specified mass. When the moving speed of the mass is greater than the critical speed, the dynamic response of the nonlinear system eventually settles to a steady state of periodic motion as seen by an observer travelling along with the mass. This is because the beam behaves like a hardening spring, i.e., the magnitude of the resisting bending moment is always larger than its linear counterpart. In order to maintain the uniform speed of the mass during the periodic vibration, the pushing force must change with time. The amplitude of the periodic vibration increases with the moving speed of the mass in the super-critical speed range. The periodic vibration undergoes a Hopf super-critical bifurcation at a nonlinear critical speed, which is slightly higher than its linear counterpart.

Applications of multifidelity reduced order modeling to single and multiphysics nonlinear structural problems

The present investigation focuses on the response of uncertain structures that are excited well beyond their linear regime so that significant nonlinear geometric effects take place. Such situations may occur due to the application of large mechanical loads but also, and especially, when the structure is part of a multiphysics problem, e.g., coupled to aerodynamics and/or heating. It is demonstrated here that the computational burden associated with the prediction of the statistics of the response can be dramatically reduced by combining nonlinear reduced order modeling and multifidelity Monte Carlo (MFMC) simulation. The MFMC approach combines the simulations of several different models of different fidelity to accurately estimates the desired statistics. This approach is well suited to reduced order models where different fidelities are easily obtained with different number of basis functions. Three such nonlinear applications are considered the first of which is a purely structural problem. The second one is a multiphysics problem, a panel undergoing a simulated high speed trajectory with aerodynamic-structural-thermal coupling. The third application is also multiphysics and focuses on the limit cycle oscillation behavior of a wing past flutter due to structural nonlinearity. In all of these applications, the MFMC performed very well leading to accurate predictions of the statistics of the response at a reduced/much reduced computational cost.

Out-of-plane stability of fixed concrete-filled steel tubular arches under uniformly distributed loads

In recent years, concrete-filled steel tubular (CFST) arches have been widely used and the out-of-plane buckling of CFST arches has become a major concern. So far, few studies have investigated the out-of-plane behaviours of CFST arches, and no codes have given the design formula of the out-of-plane stability bearing capacity. Therefore, in this paper fixed CFST parabolic arches with a circular cross-section under uniformly distributed loads are investigated. Considering the effect of material and geometric non-linearity, the distributions of the internal forces and deformations are observed, and on this basis an equivalent column model is established to derive the out-of-plane effective length coefficient. In addition, based on the stability theory, the nominalised slenderness ratio of CFST arches is modified considering the influence of rise-to-span ratios and can be substituted into any available stability coefficient equations in current design codes to calculate the out-of-plane bearing capacity of CFST parabolic arches. The proposed equation – which has a form of formula similar to the available stability equations in existing designing codes for CFST or steel members and which has an accuracy equal to or greater than the equations in the available literature – would be easier for the designers to accept and use.

Advanced computer model for analysis of reinforced concrete and composite structures at elevated temperatures

abstract: This paper is concerned on the development of a computational model based on finite element procedures for advanced analysis capable of estimating the behavior of reinforced concrete and composite steel-concrete plane structures exposed to fire. The program implemented is called NASEN, the specific thermo-structural module is used to analyze structures under fire conditions. The effects of geometric nonlinearity, material nonlinearity and nonlinear thermal gradients are incorporated into the model, as well as the degradation of material properties with increased temperature. The methodology applied for the solution is based on the unidirectional coupling of the thermal and mechanical solutions. The cross-sections of the structural elements are discretized with two-dimensional meshes for thermal analysis, while the structural analysis uses a one-dimensional beam-column element. Numerical examples are presented to demonstrate the accuracy of the computational code developed in relation to the numerical and experimental solutions found in the literature. In summary, the program adequately predicted the response of the studied structures.

A higher-order beam model for the snap-buckling analysis of FG pipes conveying fluid

The snap buckling of the FG curved pipes conveying fluid has not been reported due to the existing research on the snap-buckling problem. Therefore, the purpose of this paper is to explore this issue. First, we adopt a new high-order shear theory model and consider the thermal and geometric nonlinearity effects, and assume that the density and modulus of elasticity of the liquid are independent of temperature. Based on the generalized variational principle, the governing equation of the FG curved pipes conveying fluid is derived. Then, we assume that the FG curved pipes conveying fluid has simply supported boundary or fixed supported boundary conditions, and use the two step perturbation method to obtain the expression of the relationship between load and deflection. Then, we investigate the influence of boundary conditions, shear deformation, temperature variation, functional gradient index parameters, liquid flow velocity and geometry size on the snap buckling problems of the FG curved pipes conveying fluid. The results show that these factors have significant influence on the fluidstructure interaction problems.

Nonlinear analysis of unimorph and bimorph piezoelectric energy harvesters with flexoelectricity

This work investigates the nonlinear behaviors of nanoscale unimorph and bimorph piezoelectric energy harvesters under harmonic base excitations. In the modeling, the energy harvesters are based on cantilevered beams with tip mass, and the effects of geometric nonlinearity, inertial nonlinearity and flexoelectricity are considered. Based on the Hamilton’s principle and the theory of flexoelectricity, the nonlinear coupled governing equations of the system are derived. Galerkin’s method is employed to discrete the nonlinear equations, which are then numerically solved. Results indicate that geometric nonlinearity leads to a typical hardening nonlinear behavior of the frequency response curve while inertial nonlinearity leads to a softening behavior in contrast. In addition, influences of the tip mass and amplitude of the base acceleration on the harvesters’ electrical outputs are examined. By comparing lead zirconate titanate (e.g. PZT-5H) and polyvinylidene difluoride (i.e. PVDF) as the material for piezoelectric layers, it is found that the performance enhancement of PVDF energy harvester due to flexoelectricity is more prominent. It is also interesting to observe the flexoelectricity-induced size-dependent voltages. This work compares the performance of energy harvesters with various structures and materials, which will provide guidance for the design and optimization of piezoelectric energy harvesters utilizing flexoelectricity.