Geometric Nonlinearity Research Articles

A nose beam segmental construction process for large-span composite emergency bridges

The effectiveness of the incremental launching method with lightweight, flexible nose beam in the construction and erection of emergency bridges with large-span composite materials is investigated through a combined experimental and numerical study. A theoretical model is developed to characterize the additional bending movement induced during the flexible nose launching process and analyze stress fluctuations in structural components during critical launching stages, providing theoretical underpinning the for lightweight nose beam design. Results indicate that the stress attributable to the additional bending moment during critical launching stages constitutes approximately 9.6 %, significantly impacting lightweight nose beam design con-siderations. Additionally, it was shown that conventional static analyses are difficult to adequately capture the internal force changes during the launch of a flexible nose beam. Therefore, a finite element model accounting for geometric and contact non-linearity is proposed, exhibiting higher precision in predicting additional bending movement values compared to traditional finite element models. The accuracy of the finite element model is confirmed through scaled-down experiments.

Nonlocal strain gradient-based nonlinear vibration analysis of nonlinear FG three-phase HJCNT/MWCNT/epoxy composite microbeam resonators using a modified micromechanical model

This paper aims to study nonlinear dynamic behavior of functionally graded (FG) three-phase composite microbeam resonators made of an epoxy matrix and two reinforcements namely multi-walled carbon nanotubes (MWCNTs) and hetero-junction carbon nanotubes (HJCNTs). The effective mechanical properties of the composite microbeam are obtained using the modified Halpin-Tsai micromechanical model. The microbeam surrounding medium is simulated using a two-parameter elastic foundation. The von-Karman’s geometric nonlinearity relations are incorporated and the equations of motion are derived based on the nonlocal strain gradient Euler–Bernoulli beam model. A new closed-form analytical solution is obtained using the homotopy perturbation method. The effects of vibration amplitude, nanofiber volume fraction, nanofiber distribution pattern, small-scale parameters and the foundation parameters on the nonlinear frequency and deflection of the FG three-phase composite microbeams are studied in detail. The findings of the paper are valuable for researchers in the field of microbeam resonators.

Improved energy harvesting by enhanced nonlinearities: New phenomena and experimental demonstration

This paper investigates a nonlinear piezoelectric energy harvesting system that enhances conversion of mechanical energy to electrical energy by integrating piezoelectric materials with a nonlinear system. The research simplifies a flexible beam with macro fiber composite (MFC) piezoelectric patches using a lumped-parameter approach and derives the dynamic equations of the system using the Lagrange equations. The incremental harmonic balance method (IHBM) is then employed to solve these equations, simulating the nonlinear dynamics involved in the harvested voltage. Key findings include the initial discovery of multiple voltage islands which are voltage jumps that improve energy conversion efficiency, confirmed by experimental data validating the IHBM simulations. The study reveals that these phenomena are due to the enhanced nonlinearities of the system, particularly the geometric nonlinearity caused by the spring k1 and the nonlinear magnetic force between magnets. Adjusting k1 allows the observation of multiple voltage islands, and increasing d0 results in a broad-frequency constant voltage, offering new insights. The research concludes that the nonlinear piezoelectric energy harvester can effectively convert vibration energy into electrical one, as demonstrated by successfully powering multiple light-emitting diodes (LEDs). Bifurcation diagrams illustrate the adaptability of the system, showing transitions among periodic, quasi-periodic, and chaotic states for different parameters.

A three-dimensional finite strain volumetric cohesive XFEM-based model for ductile fracture

The verification/prediction by numerical simulation of the resistance of large-scale metal structures subjected to extreme loading (e.g. accidental mechanical overload) that can lead to failure constitutes a major issue in the transport, energy, and defense sectors. This work aims to develop a three-dimensional numerical methodology (i) capable of macroscopically accounting for the various dissipative mechanisms of plasticity and damage until failure, (ii) formulated within the framework of large deformation, (iii) implemented in a commercial computation code, and (iv) mesh-objective. The commercial computational code is ABAQUS-std, and the methodology is implemented as a user finite element (UEL). Geometric non-linearities are treated within the framework of an updated Lagrangian formulation (ULF). The more or less diffuse damage phase is described by the Gurson–Tvergaard–Needleman (GTN) microporous plasticity model with standard finite element (FE). The micro-void coalescence phase-induced dilation/shear band is described using an original volumetric cohesive extended finite element method approach (VCZM-XFEM). The progressive loss of cohesion leading to ultimate cracking is treated with extended finite element method (XFEM). Particular attention is paid to transition criteria (damage to localization, localization to cracking), to the orientation of the localization plane (especially in Mode II), to the cohesive zone model and to techniques for overcoming numerical difficulties (volumetric locking, numerical integration). The so-built 3D-FS-GTN-VCZM-XFEM unified methodology is capable of reproducing the degradation mechanisms, and, the failure surface shape and orientation in large elasto-plastic deformation of structures typical of laboratory tests, even for fairly coarse meshes.

Numerical Analysis of Combined Effect Hybrid Fibres and Fire Insulation on the Fire Resistance Performance of SCC Beams

The use of self-compacting concrete in structural members has become increasingly prevalent in various construction applications. However, these structures are susceptible to one of the most hazardous disasters, which is the fire. This paper presents a numerical investigation of the fire resistance performance of self-compacting reinforced concrete (SCC) beams, as well as a parametric study to assess the impact of hybrid fibres and fire insulation on enhancing their performance under fire conditions. The study is conducted by developing a 3D finite element (FE) model using ANSYS software, where temperatures are applied according to the ISO834 standard fire. Geometric and material nonlinearities are considered in the evaluation of the behaviour of beams under fire conditions. The developed FE model is validated by comparing the predicted results with those of the experimental tests in literature. The fire resistance performance of SCC beams was compared with that of normal strength concrete (NSC) beams. The parametric study is conducted using three types of fire insulation, namely Tyfo WR-AFP, CAFCO 300, and Carboline Type-5MD. The results showed that SCC beam has lower fire resistance performance than the NSC beam. However, the incorporation of hybrid fibres allows a 17% improvement in the fire resistance of SCC beams. The use of fire insulations has increased the fire resistance time of SCC beams, and more particularly Carboline Type-5MD insulation with an increase of 28%. The combined use of hybrid fibres and fire insulation improved the fire resistance of SCC beams by 43%.

On the nonlinear buckling and postbuckling responses of sandwich FG‐GRC toroidal shell segments with corrugated core under axial tension and compression in the thermal environment

AbstractThis paper presents an analytical approach for buckling and postbuckling analysis for functionally graded graphene‐reinforced composite (FG‐GRC) toroidal shell segments with the trapezoidal or round corrugated core under the axial tension and compression. The considered shells are placed in a thermal environment and surrounded by an elastic foundation. Based on the von Kármán‐Donnell shell theory with geometrical nonlinearities, Stein and McElman approximation, and a homogenization technique for corrugated shells, the basic equations of shells are established. The previous homogenization technique is improved by adding the thermal forces in the internal force expressions. The shell‐foundation interaction is expressed using the model of the Pasternak assumption. The Ritz energy method is used to obtain the pre‐buckling and postbuckling behaviors of the shells, from which the critical buckling tensions and compressions can be investigated. The influences of FG‐GRC face sheets, corrugated core, and foundation on the buckling behavior of sandwich shells can be shown in the numerical analysis.Highlights Postbuckling of toroidal shell segments with the corrugated core is analyzed. A homogenization technique is improved for the thermal forces in the core. The shells are made of functionally graded graphene‐reinforced composite. The nonlinear Kármán‐Donnell shell theory and Ritz energy method are applied. Special effects of input parameters on the buckling behavior are investigated.

Compressive instabilities enable cell-induced extreme densification patterns in the fibrous extracellular matrix: Discrete model predictions.

We present a new model and extensive computations that explain the dramatic remodelling undergone by a fibrous collagen extracellular matrix (ECM), when subjected to contractile mechanical forces from embedded cells or cell clusters. This remodelling creates complex patterns, comprising multiple narrow localised bands of severe densification and fiber alignment, extending far into the ECM, often joining distant cells or cell clusters (such as tumours). Most previous models cannot capture this behaviour, as they assume stable mechanical fiber response with stress an increasing function of fiber stretch, and a restriction to small displacements. Our fully nonlinear network model distinguishes between two types of single-fiber nonlinearity: fibers that undergo stable (supercritical) buckling (as in previous work) versus fibers that suffer unstable (subcritical) buckling collapse. The model allows unrestricted, arbitrarily large displacements (geometric nonlinearity). Our assumptions on single-fiber instability are supported by recent simulations and experiments on buckling of individual beams with a hierarchical microstructure, such as collagen fibers. We use simple scenarios to illustrate, for the first time, two distinct compressive-instability mechanisms at work in our model: unstable buckling collapse of single fibers, and snap-through of multiple-fiber groups. The latter is possible even when single fibers are stable. Through simulations of large fiber networks, we show how these instabilities lead to spatially extended patterns of densification, fiber alignment and ECM remodelling induced by cell contraction. Our model is simple, but describes a very complex, multi-stable energy landscape, using sophisticated numerical optimisation methods that overcome the difficulties caused by instabilities in large systems. Our work opens up new ways of understanding the unique biomechanics of fibrous-network ECM, by fully accounting for nonlinearity and associated loss of stability in fiber networks. Our results provide new insights on tumour invasion and metastasis.

Coupled higher-order layerwise mechanics and finite element formulations for laminated composite beams with active SMA layers

This study proposes a thermo-elastic coupled nonlinear finite element (FE) model for laminated composite beams with active SMA layers based on a higher-order layerwise theory and Brinson's model of SMA's phase transformation constitutive relations. The developed FE Model is further discretized by using the Newton-Raphson time integration scheme to update SMA's phase transformation progress step by step. This new model can be used for thermal-mechanical behavior analysis of hybrid SMA-composite laminated beams, which especially enables accurate prediction for static response of moderately thick to thick beams, large deformation analysis, through-thickness variations of interlaminar stresses and strains. The accuracy and effectiveness of the proposed approach are verified by several numerical examples, and the results are compared with those obtained from corresponding alternative solutions and experimental tests. Using the developed FEM, the effects of temperature, geometrical nonlinearity, pre-strain of SMA, and stacking sequence of composite laminates on the static response of hybrid SMA-composite beams are studied.

Non-linear analysis of anisotropic coated fabric utilizing Variational Asymptotic Method

The dimensional reduction of a hyperelastic coated fabric from 3D to 2D is accomplished asymptotically using the Variational Asymptotic Method (VAM). This method integrates constrained calculus of variations and asymptotics. The VAM bifurcates the analysis into two: a 1D through-the-thickness analysis and a 2D reference surface analysis. The 1D analysis leads to the derivation of an asymptotically correct 3D warping functions and a 2D non-linear constitutive law. The 2D non-linear reference surface analysis utilizes the derived 2D non-linear constitutive law to obtain 2D displacements and strains through the 2D non-linear FEA. The classification of 3D strain energy density into distinct orders is enabled by introducing two intrinsic small parameters: 1) a geometric small parameter denoted by the ratio of thickness to characteristic length (h/l≪1), and 2) a physical small parameter that ensures the largest component of 3D strain is restricted to 20 percent, which is less than 1. The model takes into account both geometric and material nonlinearities. The strain energy function, which describes the anisotropic characteristics of the coated fabric has contributions from the strain energies of fiber, matrix, and fiber-fiber interaction. The findings of the study include analytically derived 3D warping functions, a 2D nonlinear constitutive law, and the prediction of warp and weft stresses and strain for a biaxial loaded tensile specimen. These findings align with the experimental outcomes.

On the stability of prestressed beams undergoing nonlinear flexural free oscillations

We study the nonlinear free undamped motions of a hinged-hinged beam exhibiting geometric stretching-induced nonlinearity and arbitrary initial conditions. We treat the governing integral-partial-differential equation of motion as an infinite dimensional Hamiltonian system. We analytically obtain a quantitative Birkhoff Normal Form via a nonlinear coordinate transformation that yields the reduced (modulation) equations describing the free oscillations to within a certain nonlinear order with an estimate of the reminder. The obtained solutions provide a very precise description of small amplitude oscillations over large time scales. The analytical optimization of the involved estimates yields time stability results obtained for plausible values of the physical quantities and of the perturbation parameter. The role played by internal resonances in determining the time stability of the solution is highlighted and discussed. We show that initial conditions with a finite number of eigenfunctions yield bounded solutions living on invariant subspaces of the involved modes at all times. Conversely, initial conditions comprising the full (infinite) spectrum of eigenfunctions provide solutions for which time stability for all times cannot be stated.

Finite Element Analysis of Urban L-Type Sidewalk Drainage Steel Grating

In this study, structural analysis and calculations were conducted on the downward and vehicle loads to reduce vehicle accidents caused by the failure of steel gratings, and the results were compared and analyzed. To replicate the severe circumstances found in the steel grating, a vehicle load was applied at T20 and T14. Finite elements and geometric nonlinearity were applied to the material and contact in the structural analysis. As a result of the analysis, plastic sagging of the steel grating owing to the downward load and vehicle load did not occur. However, local plastic deformations occurred in the welded parts of the I-bar and crossbar. The analysis results confirm the need for strength improvements in vulnerable areas.

Predicting the dynamic response of elastic-plastic beams by dimensional analysis

Elastic-plastic beams subjected to dynamic loading are widely found in engineering. However, due to the complex coupling of geometric and material nonlinearity, there is no complete analytical solution available. In this paper, based on energy conservation and dimensional analysis, a dominant dimensionless number, the loading intensity ξ, is proposed. Including both the effects of geometry, material and load, ξ could be used to predict the significant responses of an elastic-plastic beam under uniformly pressure loading, such as energy ratio, deflection ratio and deformation mechanism. With combination of loading intensity ξ and dimensionless stiffness β, the dimensionless maximum and final deflections of elastic-plastic beams under pressure loading can be predicted directly. Dimensionless numbers of beams with different cross-sections, or under different loading forms are also analyzed and confirmed.Then, elastic effect over dynamic response of elastic-plastic beams is analyzed. For final deflection, it is found ξ>5 is the applicability of theoretical solution based on rigid, perfectly plastic (R-PP) material simplification. However, R-PP results can't be used in initial plastic hinge location and subsequent plastic zone evolution, even for very large ξ.Using these dimensionless numbers, experimental or simulation data could be expressed in a normalized and comparable form, and the physical mechanisms will be more intuitive and clearer, which is valuable for scaled dynamic tests.

Comparative analysis of a tubular masts with a 80 m high

The article presents the structures of guyed masts that are used as supporting structures. Masts of this type consist of a vertical shaft connected to the foundation by means of guy wires. The work focuses on two designs of measuring masts with an identical shaft, but with a different number of guy ropes at the level. The static analysis was carried out taking into account the geometric nonlinearity of the guy wires and environmental loads. The results of the analysis indicate how the static scheme of the structure affects its behavior. The conclusions from the work are applicable to specific designs of tubular masts, but may be an inspiration for further research on structures of this type

Stability and dynamic analyses of hybrid laminates using refined higher-order zigzag theory

This article presents a comparative study on the stability and dynamic response of hybrid laminated composite plates over monolithically produced laminated composite plates. A Refined Higher-order Zigzag Theory (RHZT) is formulated and implemented using finite element method for the analysis of hybrid laminates. This formulation considers both the interlaminar shear stress continuity and shear-free boundary conditions at surfaces of the plates. The numerical implementation employs C 0 continuous eight-noded isoparametric plate elements considering geometric nonlinearity. The element stiffness matrix is formulated to consider both the linear and nonlinear terms of the strain-displacement equations. Derivation of the consistent mass matrix for a plate element is presented following the approximation of total kinetic energy and utilising Hamilton’s principle. Numerical examples are provided to demonstrate buckling and free vibration analyses (as eigenvalue problems). The results are numerically verified and validated using data from published literature. Finally, parametric studies are presented to demonstrate the effectiveness of fibre hybridisation approach on the buckling and free vibration behaviour of laminated composites.

A robust radial point interpolation method empowered with neural network solvers (RPIM-NNS) for nonlinear solid mechanics

In this work, we proposed a robust radial point interpolation method empowered with neural network solvers (RPIM-NNS) for solving highly nonlinear solid mechanics problems. It is enabled by neural network solvers via minimizing an energy-based functional loss. The RPIM-NNS has the following key ingredients: (1) It uses radial basis functions (RBFs) for displacement interpolation at arbitrary points in the problem domain, permitting irregular node distributions. (2) Nodes are placed also beyond the domain boundary, allowing the convenient implementation of boundary conditions of both Dirichlet and Neumann types. (3) It uses strain energy in an integral form as a part of the loss function, ensuring solution stability. (4) A well-developed gradient descendant algorithm in machine learning is employed to find the optimal solution, enabling robustness and ease in handling material and geometrical nonlinearities. (5) The proposed RPIM-NNS is compatible with parallel computing schemes. The performance of this method is tested using nonlinear problems including Cook's membrane and 3D twisting rubber problems, demonstrating its remarkable stability and robustness. This work, which seamlessly integrates the neural network solvers with mechanics governing equations and computational mechanics techniques, offers an excellent alternative for nonlinear solid mechanics problems. MATLAB codes are made available at https://github.com/JinshuaiBai/RPIM_NNS for free downloading.

Solving nonlinear structural problems by associating line-search and path-following techniques

The demand for computational tools to simulate the nonlinear behavior of structures has intensified. Regarding nonlinear static or dynamic analysis, it is fundamental to use numerical strategies to trace the structure equilibrium paths, overcoming critical points (limit and bifurcations points). The nonlinear solvers must have a high level of efficiency in the two phases of the solution process (predictor and corrector), for each load step. In solving the nonlinear equations, it is quite common that Newton-Raphson's iterations do not converge or require an excessive number of iterations near equilibrium path critical points. Therefore, the line-search optimization technique appears as an additional sophistication. Basically, this technique aims to stagger the corrective displacements vector in the iterative phase, seeking to guarantee and accelerate the convergence of the process. This paper aims to verify the efficiency of the line-search technique coupled with Newton-Raphson iterations and different path-following methods and to verify their influence on the efficiency of the nonlinear solver. The effectiveness of the implemented line-search algorithm is verified by solving two slender structures with accentuated geometric nonlinearity. Such a resource is perceived to be triggered near load limit points (with more success when applied to structures with these critical points), accelerate the iterative process and increase the chances of convergence.

A novel hybrid-stress method using an eight-node solid-shell element for nonlinear thermoelastic analysis of composite laminated thin-walled structures

Composite laminated thin-walled structures, widely used in high-speed aircrafts, undergo a complex thermal–mechanical coupling environment. Geometrical nonlinearities with a thermal effect bring significant challenge to finite element analysis of structures. In this paper, a novel hybrid-stress method based on the solid-shell element is proposed for nonlinear thermoelastic analysis. An eight-node solid-shell element (CSSH8) is developed based on the assumed natural strain method and hybrid-stress formulations to overcome various locking problems and achieve an effective 3D simulation for structures with a large span-thickness ratio. The Green–Lagrange displacement-strain relation is selected to take the geometrical nonlinearities into account. The modified generalized laminate constitutive model is extended to consider both the thermal expansion and temperature-dependent material properties. A temperature variation along the laminate thickness can also be assumed in the constitutive model. Nonlinear thermoelastic equilibrium equations are derived using the Hellinger–Reissner variational principle, in which five different coupling cases for thermal–mechanical loads can be fully involved. Numerical examples demonstrate that the proposed method with CSSH8 element is insensitive to various distorted meshes and numerically robust to pass the buckling point; meanwhile large step sizes can be achieved in the path-following nonlinear thermoelastic analysis.

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.

Thermomechanical responses of steel frames under aftershock after fires

A novel advanced fiber beam-column element, which incorporates stability functions and the fiber distributed plasticity model to capture geometric and material nonlinearities, respectively, has been successfully developed to predict the nonlinear inelastic thermo-mechanical behaviors of steel frames subjected to aftershock after fires. To address the nonlinear dynamic problems resulting from aftershocks after fires, a sequential nonlinear thermal incremental-iterative solution scheme has been developed, which is based on the Newton-Raphson algorithm and Newmark-β method. In addition, a transcendental probability-based method is employed to express the statistical characteristics of aftershock intensity relative to the mainshock. The proposed method is applied to analyze three framed structures: a steel portal frame, a two-story plane steel frame, and a four-story asymmetric space steel frame. This analysis shows the accuracy, computational performance, and applicability of the proposed method. Remarkably, the results obtained from the code work, using just one or two elements per member, are in close agreement with all the results analyzed by Abaqus. This emphasizes that the proposed method effectively predicts the response of framed structures under aftershock after fires with excellent computational efficiency, significantly surpassing traditional finite element approaches in commercial software like Abaqus. The successful results of the dynamic analysis of the frames under aftershocks following fires underscore the importance of considering aftershocks after a fire incident. It is demonstrated that the occurrence of an aftershock accelerates the failure of the frame compared to the case when the frame is subjected to fire alone. This highlights the critical need to account for aftershocks when assessing the safety and structural integrity of framed structures after a fire event.

Seismic performance of shuttle-shaped double-restrained buckling-restrained brace: Experimental investigation and numerical analysis

To solve the problems of excessive cross-section size and self-weight and buckling instability of super-long buckling-restrained brace, a new lightweight shuttle-shaped double-restrained BRB (SDR-BRB) is proposed in this study. Firstly, cyclic loading experiments are conducted on three SDR-BRB specimens to investigate their failure mode and seismic performance. Then, a finite element model considering geometric, material, and contact nonlinearity is established and verified by experimental results. Finally, the effect of the restraining ratio on the hysteretic performance of SDR-BRB is studied by parameter analysis, and the restraining ratio requirement of the energy-dissipation type of SDR-BRB that meets the ductility requirements is obtained. The results show that SDR-BRB has stable and plump hysteretic curves, excellent energy-dissipation capacity, and low cycle fatigue performance, exhibiting obvious strain-strengthening characteristics. The restraining ratio is an important factor affecting the overall stability and failure mode of SDR-BRB, and it is recommended that the restraining ratio requirements of the SDR-BRB should be 2.25. The above research can provide a design reference for the practical engineering application of SDR-BRB.