Lagrangian-Eulerian Description Research Articles

Large eddy simulation investigation of the effect of radiative heat transfer on the ignition progress in a model combustor

Radiation significantly influences turbulent combustion. This paper investigates the impact of radiative heat transfer on the ignition process in a multi-staged model combustor. The ignition process is simulated both without and with consideration of radiation. Large Eddy Simulations based on the Euler-Lagrange description of the liquid spray and the Dynamic Thickened Flame model coupled with a skeletal chemical reaction mechanism are employed. The Weighted Sum of Gray Gases method are employed to solve the spectral properties and the Discrete Ordinates method is employed to solve the radiative transfer equation. The results indicate that radiative heat transfer influences the flame structure during the ignition process. In the flame propagation phase, both the total heat transfer and the exit average temperature are higher, with the radiative heat transfer during ignition being less than 15% of the total heat transfer. During the kernel generation phase, radiative heat transfer leads to a 7.24% increase in the maximum temperature of the flame kernel, a 7.74% expansion of the flame surface area, and outward movement of the position of the maximum heat release rate. Additionally, the ignition delay time extends by 14.91%. In the flame propagation phase, the flame transfers heat to the mixed gas and droplets near the flame surface through radiation, promoting flame spread.

Iron oxide nanoparticle synthesis: Simulation-based comparison of laboratory- and pilot plant-scale spray-flame synthesis

This study analyzes burner scale-dependent effects for iron-oxide nanoparticles synthesis in spray flames through a combined experimental and numerical approach. A laboratory- and a pilot plant-scale synthesis facility generate iron oxide nanoparticles from iron nitrate dissolved in ethanol/2-ethylhexanoic acid solvents on the 0.5 and 15 g/h scale, respectively. Phase Doppler measurements supply initial conditions for spray development in the numerical approach, while in situ OH* chemiluminescence and multi-line nitric oxide laser-induced fluorescence (NO-LIF) thermometry provide experimental data for comparison with simulation results of the pilot plant burner. Ex situ particle sizing by gas adsorption according to Brunauer-Emmet-Teller (BET) and transmission electron microscopy (TEM), along with phase composition determination via X-ray diffraction (XRD), are used to compare products of both burners and the corresponding simulations. The numerical approach employs a Reynolds-averaged Eulerian–Lagrangian description of the flow in combination with a flamelet/progress variable (FPV) combustion and monodisperse particle model to reflect spray-flame synthesis. Despite similar chemiluminescence between experiment and simulation, more significant discrepancies are observed in NO-LIF thermometry and particle sizing. Nanoparticle formation and growth at both burner scales is investigated using the numerical method. Special attention is directed to the high-temperature particle residence time (HTPRT). Notably, the average temperature–time profiles particles experience are almost identical in the burners, although their geometric scales and designs differ substantially. Simulation results show that while the primary particle diameter remains mostly consistent, the pilot-scale burner produces larger particle agglomerates than the laboratory burner. The difference is attributed to an increased particle number concentration during the initial formation of soft agglomerates. The findings demonstrate that, despite retaining a similar HTPRT, the overall flow conditions and liquid spray dispersion, which impact the distribution of the particle number concentration, influence the final agglomerate size.

Finite Element Analysis of Nonlinear Contact Problems with Mixed Eulerian-Lagrangian Description

<p class="Abstract">This study deals with analysis of structures using mixed Eulerian-Lagrangian description. Apart from generally used Lagrangian description which uses initial configuration as reference, the newly proposed uses one of actual configuration as reference. Therefore, the total displacement is decomposed into two portions, i.e., the portion covering displacement from initial into referential configuration called Eulerian displacement, and the portion covering displacement from referential configuration into current configuration called Lagrangian displacement. The new technique is suitable to be applied to several classes of structures such as frictional contact and tensile structures. Eulerian displacement is used to represent relative displacements between material points paired in a nodal point in which slip mode occurs, while Lagrangian displacement is used to represent mutual displacement of material points paired in a nodal point in which stick mode occurs. The method was applied to certain contact problems, and the results obtained agreed fairly well with existing results found in references.</p>

Extraction of Lagrangian Coherent Structures in the framework of the Lagrangian–Eulerian Stabilized Collocation Method (LESCM)

In recent years, the investigations on Lagrangian Coherent Structures (LCS) in complex flows have attracted increasing attention due to their ability to accurately describe flow field details. In this study, we propose a novel and accurate numerical technique based on the Lagrangian–Eulerian Stabilized Collocation Method (LESCM) for computing the Finite Time Lyapunov Exponents (FTLEs), which is essential for extracting LCSs in viscous incompressible flows. LESCM, previously employed for simulating fluid–structure interaction problems, was developed based on the Material Point Method (MPM). The hybrid Lagrangian–Eulerian​ description in LESCM enables explicit tracking of fluid flow trajectories throughout the simulation and direct evaluation of the FTLE field. Furthermore. The errors in FTLEs caused by the Particle Shifting Technique (PST) are completely avoided due to the Eulerian characteristic of LESCM as the deformation gradient is calculated based on fixed Eulerian nodes rather than fluid particles with unphysical shifting. Consequently, the novel technique based on LESCM surpasses the accuracy of pure Lagrangian particle methods and provides an accurate way of detecting complex LCSs in flow fields. Additionally, By harnessing the remarkable efficiency of LESCM, MATLAB can now handle up to 16 million particles with ease, eliminating the need for parallel computation techniques. Several numerical examples, such as 2D Taylor-Green​ vortices, flow passing a circular cylinder and a 3-dimensional shear driven cavity problem, have been tested to demonstrate the effectiveness of this novel approach under various conditions.

Tension Characteristics of Cable-Driven System Based on ALE Formulation

This paper mainly studies the tension characteristics of cables in Cable-Driven Parallel Mechanisms (CDPMs). The exact catenary model and cable model based on the Arbitrary Lagrangian Eulerian description (ALE) are used. First, the ALE cable model and the exact catenary model are used to analyze and compare the tension at each point of a single cable, which proves the calculation accuracy of the ALE cable model. Then, the cable model described by ALE is used to model the Cable-Driven Parallel Mechanisms, the end effector is enabled to do a specific helical motion, the tension characteristics of the cable are extracted and analyzed, and the mesh independence of the ALE elements and calculation convergence are verified.

Conservation and accuracy studies of the LESCM for incompressible fluids

Conservation properties are very important for numerical methods. The presence of non-conservative solutions can result in fictitious sources or sinks that cause alterations in the flow balance. In this paper, the conservation properties and their influences on the accuracy of a newly proposed meshfree Lagrangian-Eulerian stabilized collocation method (LESCM) for the incompressible fluid flow are mathematically derived and numerically validated. The LESCM inspired by the material point method (MPM) is based on the hybrid Lagrangian-Eulerian description, in which the accuracy of the solution on Eulerian nodes and the mapping between Eulerian nodes and Lagrangian particles are highly associated with the conservation properties. On one hand, since the Navier-Stokes equations are solved without any truncation or simplification, the global conservation can be satisfied like most of the numerical methods during the solution on the Eulerian nodes. Moreover, this method can also meet the global conservation for the mass, linear momentum and angular momentum during the mapping process which are detailedly derived in the paper. After that, the energy conservation is evaluated by the corresponding equation. On the other hand, the local conservation properties of the discrete equations as well as the mass and momentums can be satisfied in the LESCM, while most of the numerical methods do not possess this property. Therefore, the conservation properties can be maintained during both the solving and the mapping processes which guarantee the high accuracy, optimal convergence and good stability of the LESCM method. Numerical examples of steady-state flow, shear-driven cavity, dam break and water sloshing problems with complex free surface and breaking waves, demonstrate the high accuracy and efficiency as well as conservation of the LESCM. It also performs very well for fluid flow problems with large Reynolds numbers. This method can be extensively applied to the engineering problems associated with the incompressible free surface flow.

Transport mechanism of temporary plugging agent in complex fractures of hot dry rock: A numerical study

Hydraulic fracturing with temporary plugging agents is one of the most promising technologies to improve the thermal efficiency of deep geothermal reservoirs. Understanding the migration and plugging mechanism of temporary plugging agents in artificial fractures is the key to successful fracturing operations. However, there is currently a lack of understanding of the high temperature effect on the migration of temporary plugging agents in fractures. Therefore, based on the Eulerian-Lagrangian description framework, this paper uses the computational fluid mechanics (CFD)-discrete element method (DEM) two-way coupling algorithm to establish a multiphase flow model for the migration of temporary plugging agents in complex fractures. We carried out relevant numerical simulation research and compared with the experimental results. Numerical simulation results show that the main factors affecting the migration of temporary plugging agent include formation temperature, fracture complexity, viscosity of carrier fluid, mass concentration of temporary plugging agent, flow regime of the carrier fluid, and inter-particle friction coefficient. Among these factors, the high temperature effect reduces the amount of temporary plugging agent entering complex branch fractures, thus weakening the plugging efficiency of temporary plugging agent for branch fractures. However, the adverse effect of high temperature on plugging can be overcome by increasing the injection rate of temporary plugging agent and increasing the width of the fracture to improve the plugging efficiency of branch fractures. The numerical results provide important theoretical and practical significance for the design scheme of temporary plugging and diverting fracturing in hot dry rock.

Cooperation and Coordination Transportation for Nonholonomic Mobile Manipulators: A Distributed Model Predictive Control Approach

This article addresses the problem of cooperation and coordination transportation for decoupling nonholonomic mobile manipulators (NMMs) in a workspace with obstacles. We propose a distributed model predictive control (MPC) approach for a team of NMMs to transport a target object while satisfying significant constraints and limitations, such as the feasible state and control input constraints, parameter synchronization constraints, and obstacles within the workspace. First, under the framework of the decoupling dynamics, an auxiliary dynamics model for task-space end-effectors and null-space mobile bases is obtained by the nonlinear feedback technique based on the Euler–Lagrange description of the NMMs. Using the modified virtual structure method, the cooperation and coordination transportation problem for NMMs is simplified as two independent synchronization tracking control problems for task-space end-effectors and null-space mobile bases. A distributed constrained optimization problem is established by taking the parameter synchronization and system constraints into the cost function. A general projection neural network (GPNN) approach is employed to solve the optimization problem and obtain the optimal control input. Moreover, a sufficient condition that guarantees the stability of the closed-loop system is further developed. Simulation results show that the proposed cooperation and coordination transportation strategy is feasible and effective.

ALE-ANCF modeling of the lowering process of a J-lay pipeline coupled with dynamic positioning

A novel structural dynamics model for the lowering process of a J-lay pipeline is established by combining the absolute nodal coordinate formula with the arbitrary Lagrangian–Eulerian description. The constraint on the top of the pipeline is introduced into the dynamic equation in the form of generalized coordinates by using a material transport boundary to simulate the lowering process of the top end of the pipeline. A mesh scheme is adopted to control the element length and prevent numerical disturbances. The accuracy of the material transport boundary and mesh scheme is verified for the case of a pendulum with a time-varying length. Then, a coupled analysis program is developed to investigate J-lay deployment by a vessel using dynamic positioning. The tensioner is modeled as a damper to adjust the pay-out speed of the upper end of the pipeline. The numerical analysis is carried out on an explanatory example of a 16-inch pipeline being laid at a 1000-m water depth. The results show that the lowering process strongly affects the dynamic characteristics of the touch-down zone.

An efficient and high-fidelity local multi-mesh finite volume method for heat transfer and fluid flow problems in metal additive manufacturing

The multi-scale and nonlinear feature of additive manufacturing problems poses great challenges to numerical algorithms regarding computational efficiency and fidelity. In this work, we propose a novel local multi-mesh finite volume method for heat transfer and fluid flow problems in the additive manufacturing process. In this method, two sets of meshes (coarse base mesh and finer overlay mesh) are used to resolve the macroscopic temperature field of the whole domain and the mesoscopic heat transfer and fluid flow problem within a relatively small region covering the melt pool, respectively. The interaction between the base mesh and the overlay mesh is handled by the Dirichlet boundary conditions on the interface following the refinement-by-superposition idea, such that the powder-scale simulation is available with high efficiency. The finer mesh with cells of sub-powder size uses the arbitrary Lagrangian–Eulerian description and moves with the heat source to keep coverage of the region with high solution gradients. According to the moving feature of the finer mesh, a particle-volume fraction conversion scheme is introduced to update the material distribution. The local multi-mesh finite volume method is further combined with the discrete element method as well as a surface reconstruction method to alternatively solve the powder layering process and the laser melting process. A set of numerical cases is presented, and the numerical results are compared with analytical and experimental data from the literature, with good agreement in cases where such data is available. Moreover, the computational efficiency of the proposed method is proved to be dozens of times (16∼50 for the given size ratios of the melt pool to the whole domain) of the finite volume method using a uniform structured mesh. It is expected to be a powerful tool for efficiently achieving powder-scale simulation of the additive manufacturing process and other similar multi-scale problems.

Large deformation analysis of shell-type structures using the VDQ-transformed scheme: A two-point formulation based on 3D elasticity

Shell-type structures are frequently used in aerospace, marine and civil engineering. In this paper, a numerical approach called as VDQ-transformed is introduced to analyze the large deformations of hyperelastic shell-type structures based on the Saint Venant–Kirchhoff constitutive model in the context of three-dimensional (3D) nonlinear elasticity. According to the Euler–Lagrange description, the kinetic first Piola-Kirchhoff tensor and kinematic deformation gradient tensor are considered for the stress and strain measures in the formulation. By replacing the tensor form of formulations with matricized ones, the governing equations are written in a novel vector-matrix format which can be readily exploited for programming in numerical approaches. Moreover, discretizing is carried out by the variational differential quadrature (VDQ) method as a point-wise numerical method. To apply the VDQ technique, a transformation is used to map the irregular domain into the regular one. Some well-known benchmark problems for the large deformations of shells are solved to assess the approach. Compact matricized formulation, simple implementation, being locking-free, computational efficiency and fast convergence rate can be mentioned as the main features of the introduced numerical approach.

Waveguide finite element modelling for broadband vibration analysis of rotating and prestressed circular structures: Application to tyres

This paper deals with the waveguide finite element (WFE) method for broadband vibration analysis of rotating and prestressed circular structures. The equilibrium equations governing the vibration problem are formulated by means of a mixed Eulerian–Lagrangian description, allowing to rigorously include the effects of Coriolis, centrifugal and prestress efforts. The inflation pressure is also rigorously described by a follower pressure load at the fluid–structure interface. Due to Coriolis acceleration, solving the free response of the rotating system leads to a quadratic eigenproblem, which can be transformed into a linear eigenvalue problem. The forced response relies on modal decomposition accounting for specific properties of the eigenproblem. A simplified form of viscous damping is proposed, enabling to set damping factors for each mode, while preserving the symmetry of the undamped problem matrices. The WFE model qualitatively compares with an analytical model of a rotating circular shell from the literature. The WFE model is applied to the vibration of a rotating tyre with heterogeneous cross-section up to a frequency of 4 kHz. With rotation the dispersion curves become asymmetric. The waves propagate faster downstream than upstream due to the combined effect of Coriolis acceleration and Doppler shift. The effect of rotation is also clearly pointed out with point and transfer mobility results, showing higher amplitude downstream than upstream. Some dominant mode shapes over the considered frequency range are finally presented and discussed. The results of this study exemplify the efficiency of the WFE approach for broadband vibration analysis of rotating tyres.

A Novel Decomposition Approach Preventing Spurious Entropy Generation in Hybrid Thermoacoustic Stability Computations

Abstract Prominent approaches for the computation of thermoacoustic stability are hybrid methods like the linearized Navier–Stokes equations (LNSE) or the linearized Euler equations (LEE). The transient fluctuations around a precomputed steady-state mean flow field solved with these sets of equations naturally include the energy transition between acoustic, vertical, and entropic modes. It is common practice to account for flame-acoustic interactions by applying measured or computed flame transfer functions (FTF) as a volumetric source term proportional to the mean heat release rate in the energy equation. However, the underlying assumption of a static flame is the root cause of spurious entropy production, which may ultimately falsify the thermoacoustic stability predictions. In the present paper, a methodology to include arbitrary flame movement in the governing set of equations is presented. The procedure makes use of an arbitrary Lagrangian-Eulerian (ALE) description of conservation equations and is demonstrated for the Euler equations. The resulting set of linear perturbation equations is then applied to two test cases. First, the frequency response of a one-dimensional premixed air-methane flame is evaluated. Secondly, the frequency response of the first longitudinal eigenmode of an experimental premixed, swirl-stabilized combustor is computed. To demonstrate the reduction of spurious entropy waves, the results are compared to those of the classic LEE.

An edge‐based smoothed finite element framework for partitioned simulation of vortex‐induced vibration problems

AbstractThis article proposes an edge‐based smoothed finite element method (ESFEM) for predicting vortex‐induced vibration (VIV) of multiple rigid and elastic structures. The ESFEM is applied to discretize the Navier–Stokes and elastodynamic equations with three‐node triangular (T3) element. The fluid excitation is also evaluated in the edge‐based notion. New integration points are arranged in local smoothing domains to ease the resultant approximation. Dynamic grids are moved by an efficient two‐level mesh scheme. The fluid‐structure mechanical system is formulated under the arbitrary Lagrangian–Eulerian description which enables tight coupling of interacting fields in a partitioned way. Especially, the geometric conservation law is respected for the ESFEM through a mass source term constructed in the T3 element context. The developed technique is validated against previously published data for three low‐Reynolds‐number VIV problems. Flow features and structural responses have been correctly identified therein as a result of the numerical prediction.

Recent advances in hybrid Eulerian–Lagrangian description of atomization

AbstractAtomization of liquid fuel is a crucial process to energy utilization. A thorough understanding of the physics of liquid atomization is challenging to acquire but necessary. During the past decades, numerical simulation methods for atomization with interface capturing schemes have been developed rapidly. However, several remaining issues need to be highlighted, such as the minimum size of the droplet to capture, numerical mass defects, and others. Thus, those simulations have been mostly limited to the primary breakup process and cannot capture the huge number of tiny droplets during the secondary breakup process. In recent years, a Eulerian–Lagrangian description of atomization has been introduced for the multi‐scale modelling of its whole process, in which the primary atomization process is treated in the Eulerian framework while the secondary atomization is treated in the Lagrangian framework. This hybrid method has been demonstrated to have many advantages in accuracy and efficiency. Considering its wide applications and contribution to the field, a comprehensive review is made in this work. First, an introduction to the phenomenon of atomization and the development of atomization numerical simulation in recent decades is made. Governing equations in the Eulerian and Lagrangian frameworks are then summarized. This is followed by a discussion of the hybrid combination method, the numerical framework, and its applications in atomization simulations. Last but not least, several relevant issues demanding attention are discussed as well.

A highly efficient and accurate Lagrangian–Eulerian stabilized collocation method (LESCM) for the fluid–rigid body interaction problems with free surface flow

A Lagrangian–Eulerian stabilized collocation method (LESCM) for the fluid–structure interaction problems involving free surface flow is presented in this work, in which the structure is modeled by a rigid body. This method is an evolution of the material point method and particle-in-cell methods which are based on the hybrid Lagrangian–Eulerian description. The problem domain of the fluid and structures is discretized into the Lagrangian particles which carry the information, and the problem domain covering the entire movement space is discretized into the uniformly distributed Eulerian background nodes. The coupling governing equations of the fluid, structures and interfaces are solved by the meshfree stabilized collocation method (SCM) employing the reproducing kernel (RK) approximation on the Eulerian nodes. The solution is very efficient since the Eulerian nodes are set to be the initial positions in each time step and it is no need to reconstruct the shape function. The information mappings between the Lagrangian particles and the Eulerian nodes are also conducted by the RK approximation which can keep the mass and momentum conservation of the solution. The cell-cut algorithm is introduced to couple the fluid and the structures which can solve the fluid pressure and the fluid–structure interactional force simultaneously and avoid the complicated iterations of the traditional interaction algorithms. Several numerical examples including the collapse of water column with a rigid barrier, water entry of a half-buoyant circular cylinder and a rigid box rotating and sinking in water are simulated, which demonstrate the high accuracy, high efficiency and good stability of the proposed method. This method can be extensively applied to the engineering applications of fluid–rigid body interactions.

Investigation of the retrieval dynamics of the tethered satellites using ANCF-ALE variable-length element

Tether satellite system (TSS) comprises two satellites connected by a flexible tether and has wide applications, such as orbital transferring, deep space exploration, and so on. In this paper, a variable-length element, based on the absolute nodal coordinate formulation (ANCF) in the framework of arbitrary Lagrangian-Eulerian (ALE) description, is used to predict the characteristics of length variation and flexibility of the tether in the phases of retrieval and station-keeping. Then, to achieve a stable retrieval implementation and take the under-actuation property of the TSS into account, an optimal retrieval trajectory is programmed using the Gauss pseudo-spectral method based dynamic optimization. Three different retrieval schemes are implemented using the developed ANCF-ALE model. Numerical studies show that, compared with the dumbbell model, the ANCF-ALE based model can predict the tension of the tether in the phase of retrieval. Results indicate that the tether tension is sensitive to the ratio of change of the tether retrieval velocity. Improper retrieval scheme may induce the intensive oscillation in the tether tension, or a switched state of the tether between pseudo-slack and tensile. In the optimization for optima trajectory programming, weight of ratio of tether velocity in the objective function should be considered carefully to realize a robust retrieval implementation.

Large-Eddy Simulation of Flame Dynamics During the Ignition of a Swirling Injector Unit and Comparison With Experiments

Abstract During the ignition of a swirled single-injector combustor, two phases have been identified experimentally. In the first, the flame penetrates the injection unit, while in the second, the flame lifts off after a substantial delay before stabilizing at a distance from the injector. This transient phenomenon is investigated using Large Eddy Simulations based on an Euler–Lagrange description of the liquid spray, an energy deposition model to mimic ignition, and the thickened flame combustion model. It is shown that the initial penetration of the flame in the injector unit is linked with the positive pressure excursion induced by the rapid volumetric expansion of burnt gases. This sudden expansion is itself due to the fast increase in heat release rate that occurs during the initiation of the process. The corresponding positive and negative pressure disturbances induce a rapid reduction of the mass flow rate through the injector, followed by an acceleration of the flow and a return to the nominal value. It is also shown that the flame root disappears after another delay, which results in the flame edge lifting and stabilization at a distance from the injector exhaust corresponding to steady operation of the device. The relatively long delay time before this liftoff takes place is found to correspond to the residence time of the cooled burnt gases in the vicinity of the chamber walls, which are ultimately entrained by the internal recirculation zone and quench the lower flame foot.

Effects of Orbital Perturbations on Deployment Dynamics of Tethered Satellite System Using Variable-Length Element

Orbital perturbations caused by the space environment will induce deviations compared with the prescribed motion trajectory or dynamic performance of the tethered satellite system (TSS). To comprehensively investigate the effects of the orbital perturbations on the TSS, a precise variable-length element that can describe the large deformation and flexibility of the tether is adopted in this paper to predict the deployment dynamics considering orbital perturbations, including atmospheric drag, solar pressure, lunisolar gravitation, and J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> perturbation. To this end, the variable-length element using arbitrary LagrangianEulerian (ALE) description in the frame work of absolute nodal coordinate formulation (ANCF) is developed firstly. Subsequently, the dynamic governing equations for the TSS are established in the context of ANCF with the employment of ANCF reference node (ANCF-RN). Effects of orbital perturbations including atmospheric drag, solar pressure, lunisolar gravity and J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> perturbation on the dynamics of an optimal deployment are analyzed numerically. It is shown that the orbital perturbations except the J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> perturbation will induce the out-of-plane motion of the TSS. Additionally, the tether tension is less affected by the orbital perturbations. By contrast, the lunisolar gravitation will induce a deviation on the motion path of satellite, which should be considered in the design phase of the TSS.

Nonlinear bending analysis of hyperelastic Mindlin plates: a numerical approach

In this paper, a numerical solution strategy is proposed for studying the large deformations of rectangular plates made of hyperelastic materials in the compressible and nearly incompressible regimes. The plate is considered to be Mindlin-type, and material nonlinearities are captured based on the Neo-Hookean model. Based on the Euler–Lagrange description, the governing equations are derived using the minimum total potential energy principle. The tensor form of equations is replaced by a novel matrix–vector format for the computational aims. In the solution strategy, based on the variational differential quadrature technique, a new numerical approach is proposed by which the discretized governing equations are directly obtained through introducing differential and integral matrix operators. Fast convergence rate, computational efficiency and simple implementation are advantages of this approach. The results are first validated with available data in the literature. Selected numerical results are then presented to investigate the nonlinear bending behavior of hyperelastic plates under various types of boundary conditions in the compressible and nearly incompressible regimes. The results reveal that the developed approach has a good performance to address the large deformation problem of hyperelastic plates in both regimes.