Principle Of Potential Energy Research Articles

Multiple equilibria of pinned FGP-GPLRC circular arches under a half-span distributed radial load

This article presents a theoretical analysis on the multiple equilibria of pinned functionally graded porous graphene platelet reinforced composite (FGP-GPLRC) circular arches subjected to a half-span distributed radial load. The effective material properties of the arch with different porosity distribution modes are approximated via a modified Halpin–Tsai micromechanical model. The decoupled neutral-plane-based governing equations are then built in the framework of the principle of minimum potential energy, from which analytical solutions for the radial displacement at an arbitrary point on the arch axis are derived. Utilizing a perturbation method, the possible buckling modes are discussed. The complete buckling evolution process of bending moment and vertical displacement are followed, meanwhile the critical geometrical parameters that control buckling behaviors switching are identified. To validate the presented analytical solutions, Finite element (FE) analysis is carried out. An in-depth parameter analysis is performed subsequently to evaluate the fluences of porosity distributions, GPL weight fraction, and porosity coefficient on the multiple equilibria path of arches. It was found that the pinned FGP-GPLRC arches could buckle only in a limit point mode under a half-span distributed radial load. When λ ≥ 8.36 , the multiple equilibria phenomenon occurs and the external force corresponding to inflexion point vanishes.

A numerical investigation of thermal stress induced cracking pattern in the solidifying nuclear fuel droplet during MFCI

During Molten Fuel Coolant Interaction (MFCI) occurring in a Sodium-cooled Fast Reactor (SFR) following a severe accident, the corium jet breaks up into coarse droplets due to hydrodynamic instabilities and fine flaked debris are generated due to the thermal stress cracking occurring on the solidifying droplet. In particular mixed oxide core debris quenched by liquid sodium are more prone to thermal stress cracking because of the excellent heat transport properties of liquid sodium, which leads to a large temperature gradient across the crust of the ceramic fuel. In this paper, thermal stress initiated cracking of solid crust of the nuclear fuel droplet is studied using Fracture Bifurcation Theory (FBT) and Minimum Potential Energy Principle (MPEP). FBT is able to predict the minimum crack length needed for crack propagation or catastrophic failure depending on the computed KI values. On the other hand, MPEP can predict the periodic and hierarchical cracking pattern that can develop on the core debris. This helps in the prediction of number of cracks and the crack length that can develop on the solid crust. Parametric studies have been carried out by varying MOX droplet sizes, crust thickness and cooling conditions and calculating KI by semi-analytical means and comparing it with KIC. The analysis revealed that solidifying droplets with radius equal to or more than 2 mm are susceptible to thermal stress initiated crack growth and catastrophic breakage even if a few tens of micron size initial crack develops on its surface. Then a particular case of 2 mm radius core debris is considered and its cracking pattern is studied by applying MPEP. This optimal crack configuration is obtained by minimizing potential energy for a given range of crack length and spacing. The analysis has been carried out with ANSYS APDL code which calculates the strain energy for a given initial crack length and spacing. The 2D computational model is validated with a similar study carried out for Alumina disc quenched in water and the results are in good agreement. The minimum fine fragment size predicted by the analysis for mixed oxide debris is a flake like debris with equivalent radius of 41 µm when approximated to be a sphere. The particle size correlates well with the fine debris sizes reported in literature of MFCI experiments.

The stress state of a plate with several holes under the action of axial tensile load

The purpose of the research is to develop a numerical method for determining the stress state of plates with several holes. The research approach is based on the development of the superposition method for singular solutions. The study objective is to solve a practical problem of determining the stress concentration coefficients in a plate with two holes of the same diameter. The study uses the numerical method of elasticity theory in the form of a superposition of four special solutions, each of which lies entirely within the corresponding hole contour. The resulting contour integrals in the displacement formula are replaced by their approximate values using the M-point trapezoidal formula or the Gaussian quadrature formula. Equating to zero the expression in variations of unknown constants (the principle of minimum potential strain energy), we have obtained a system of linear algebraic equations 4MN of unknown distribution densities. After determining the constants using known formulas, the stress-strain state of the plate with holes can be calculated. The error of the developed method is no more than 0.6% compared to the known solution.

Cross-well dynamics for vibration energy harvesting of base-excited antisymmetric bi-stable laminate with a point being fixed

The cross-well dynamic of the bi-stable laminates triggered by ambient vibration is a typical nonlinear dynamic, the larger deformation makes the bi-stable laminates attract much attention in vibration energy harvesting. To obtain the performance of cross-well dynamics and vibration energy harvesting of the bi-stable laminate theoretically, a 4-layer harmonic base-excited antisymmetric cross-ply bi-stable laminates with d31 type Marco fiber composite (MFC) for vibration energy harvesting is proposed. The bi-stable laminate is fixed at a chosen point where a base excitation is applied as displacement excitation. The first order shear deformation laminated plate theory (FSDT), geometric nonlinear, and the energy principle are employed to obtain the governing equation of the system in terms of the polynomial coefficients of configuration functions. Two stable configurations are calculated by the principle of minimum potential energy, which is used as the initial state for the energy harvesting analysis. The stable configurations are predicted, and evaluated by comparing them with ABAQUS. The cross-well nonlinear dynamic behaviors and the performance of energy harvesting are analyzed. The effects of excitation level, excitation frequency, and the position of the fixed point on the cross-well dynamics and energy harvest characteristics of the antisymmetric bi-stable laminates are investigated in-depth, and some new aspects are revealed. It demonstrates that the base displacement harmonic excitation can induce chaotic cross-well vibration in a high-frequency band when the fixed point is far away from the center point, the various cross-well vibration of the system is more likely to occur in the dominate-frequency resonant band.

The random thermo-elastic nonlinear vibration analysis of porous FGM nano-beams using the first order perturbation theory

The objective of present work is to study the nonlocal nonlinear thermo-elastic vibrations of porous nanobeams made up of functionally graded material (FGM) with random material properties. The mechanical properties of the nano-beam are calculated using a porosity based power law model by assuming the cosine type porosity distributions. The randomness present in the material properties cause the mechanical characteristics of the nano-beams to be random, hence first order perturbation theory has been employed to take care of this randomness. The Reddy’s beam theory in association with the Eringen’s non classical elasticity has been used to account for nonlocal effects, and Von-karman nonlinearity has been employed to take care of geometric nonlinearity. The governing equations are derived from the minimum potential energy principle and solved them using the finite element method. To validate the present model, a convergence and comparison study has been performed. Further, the effects of amplitude ratio, aspect ratio, uncertain material properties, size parameter, porosity, thermal environment, and gradation of material on the stochastic behavior of the porous FGM nano-beams are demonstrated. As a result of the present research, the significance of considering thermal environment, porosity, and random material properties has been revealed for the design of nanodevices and systems to be more reliable.

Innovative energy storage system harnessing gravity and electromagnetic for sustainable power solutions

AbstractIn the face of increasing global energy demand and growing dependence on renewable sources, there exists a compelling need for innovative energy storage solutions. Traditional methods, while effective, face limitations in terms of scalability, adaptability, cost, and environmental impact. This urgency is particularly evident in the intermittent nature of renewable sources like solar and wind. To bridge the gap between energy production and demand, there is a compelling call for innovative storage technologies that not only overcome current limitations but also align with the evolving landscape of sustainable energy solutions. This short communication introduces a preliminary design concept for an innovative energy storage system (ESS) designed to store excess electrical energy generated during off‐peak periods, particularly from renewable sources, for subsequent retrieval during peak demand. The proposed storage solution capitalizes on the principles of electromagnetic induction and gravitational potential energy, providing an inventive and sustainable approach to energy storage. The proposed ESS can promise a swift and effective storage solution, particularly for remote, off‐grid areas, boasting high energy autonomy, minimal maintenance requirements, and negligible environmental impact. The preliminary design specifics and distinctive features of the proposed ESS are outlined, along with a discussion on the challenges associated with its development and implementation.

Bending analysis of FGSP nanoplate resting on elastic foundation by using nonlocal quasi-3D theory

In this paper, the bending response of a functionally graded saturated porous (FGSP) nanoplate resting on the Pasternak elastic foundation is analyzed within the framework of quasi-3D higher-order shear deformation theory (quasi-3D HSDT) for the first time. The material properties are presumed to change gradually along the thickness direction following three patterns of porosity distribution: uniform, non-uniform symmetric, and asymmetric. The theory of poroelasticity developed by Biot is utilized in modeling the stress-strain relationships for the saturated condition. Moreover, the nanoscale effects of the structures are considered by Eringen's nonlocal elasticity theory. The governing equations are derived by using the principle of minimum potential energy according to quasi-3D HSDT, which ensures transverse shear stress-free on the upper and lower surfaces of the nanoplate. Based on the obtained closed-form solution, the impacts of the porosity distribution patterns, porosity coefficient, Skempton coefficient, geometrical parameters, elastic foundation, and nonlocal parameters on the bending behavior have been explored. According to the findings, when the pores are saturated by the fluid, the plate stiffness increases. Additionally, increasing the values of the nonlocal parameter for FGSP nanoplates leads to an increase in deflection and stresses. Finally, the present study quantitatively reveals the size-dependent effects of a saturated porous medium.

On the gradient-enhanced damage model for a hyperelastic material

An approach for modeling damage in the material in a geometrically nonlinear setting is studied. We consider a gradient-enhanced damage approach where the damage variable is taken as an independent variable, and the fluxes conjugated to the damage gradient are computed. The concept of maximum dissipation is used to derive the global Kuhn–Tucker conditions. The total free energy function consists of two nonlocal terms corresponding to referential gradient of the nonlocal damage variable and a penalty term to bridge the local damage variable and the nonlocal damage variable. Based on the principle of minimum total potential energy, a coupled system of Euler–Lagrange equations is obtained and solved in weak form. These nonlinear system of equations is solved by a standard Newton–Raphson-type solution scheme. The regularization capabilities, as well as the accuracy and efficiency of the proposed damage models are demonstrated by some standard benchmark examples.

Elastic and inelastic major-axis flexural buckling of cellular steel columns

This study investigates the elastic and inelastic major-axis flexural buckling of cellular steel columns. Based on the stationary principle of potential energy, the existing elastic buckling load equation is refined to incorporate the local bending deformations at web posts. The column strength curve for determining the critical loads is then derived. For the elastic buckling, the refinement provides a significant improvement. For the inelastic buckling, the effects of residual stresses and initial geometric imperfections on the column strength are examined by the validated nonlinear finite element (FE) models. The initial geometric imperfection amplitudes of L/300 and L/500, where L is the column length, are recommended for global buckling of cellular steel columns fabricated from the parent steel shapes with h/b ≤ 1.2 and h/b > 1.2, respectively, where h/b is the depth-to-width ratio of the parent steel shapes. The developed column strength curve conservatively predicts the major-axis flexural buckling strength of practical cellular steel shapes, with an average prediction-to-FE buckling stress ratio of 0.97. A comparison also shows that the current EC3 and AISC360 equations are applicable for predicting the strength of practical cellular columns, provided that the refined elastic buckling load is adopted.

On the distribution of tangential mass forces in the Earth's lithosphere

The study aims to determine and interpret the distribution of the global tangential mass force (TMF) vector field by azimuthal orientation and intensity. Using cluster and correlation analysis, we compared the direction of the TMF vector field with the direction of movement of permanent GNSS stations and the direction of movement of the GSRM model continental velocities from the Global Strain Rate Map Project. Methodology. The author continues their study of additional planetary stresses in the lithosphere caused by distributed mass forces. The forces in question may be linked to the repositioning of the Earth's lithosphere, which can create stresses aimed at aligning the distribution of lithospheric masses with the geoid's figure. This repositioning happens through the mechanism of gravitational forces and the principle of minimum potential energy. The presence of a deviation of the plum line from the normal to the surface of the solid Earth determines the appearance of TMF acting in the upper shell of the Earth. It is proposed to calculate the amplitudes and directions of the vectors of such TMF based on data regarding the difference in the parameters of two global ellipsoids that approximate the physical surface of the lithosphere and the geoid. Originality. For the modern era, the value of the angle of rotation between the smallest axis of the ellipsoid approximating the surface of the lithosphere and the axis of rotation of the Earth is 2.6°. The distribution of the TMF vector field is consistent with the contours of the continents, i.e., the arrows of the vectors indicate the directions of lateral movement of tectonic plates and the movement of continents during the Earth's evolution. As a result of the change in the orientation of the ellipsoid describing the lithosphere, an updated field of potential horizontal forces is formed, which, by the conservation of the momentum of motion, move lithospheric masses and generate stresses and deformations in the lithospheric shell. Since the TMF has different directions and intensities, a cluster analysis of the TMF distribution was performed. It revealed certain regularities in the distribution of these parameters. We also compared the directions of the TMF vector field with the directions of movement of permanent GNSS stations and the directions of movement of model velocities of the continents of the GSRM (digital model of the tensor field of the global velocity gradient). Scientific novelty. The study detailed the peculiarities of the connection between the directions of the TMF vector field, the directions of movement of permanent GNSS stations, and the ones of the model velocities of the GSRM continents. Studies of the TMF, which arise as a result of the reorientation of the thin solid shell of our planet, have shown that a deformation field of shear is formed on its surface. In our opinion, this is one of the likely factors of the process that triggers global movements of lithospheric blocks. As a result, the shape of the lithosphere is transformed, which is characterized by a change in the size of the axes of the ellipsoids describing the surface of the lithosphere and their orientation. Practical significance. The research results make it possible to more reliably interpret the peculiarities of the TMF distribution. These forces can trigger mechanisms for discharging accumulated stresses, which is important for studying seismicity.

Modeling and analysis of radial throw of micro-milling tool based on tool-attachment errors in high-speed rotating

In the process of micro-milling complex structures, radial throw is likely to cause lower dimensional/form accuracy, which will severely affect the performance of the components. Therefore, it is necessary to investigate the source contributing to the radial throw. According to the kinematic process of the radial throw arising from the attachment errors of the micro milling cutters, a mathematical model considered the attachment errors and the variable section geometry of the micro milling cutters was established to predict the radial throw on the basis of the principle of minimum total potential energy and the Timoshenko beam theory. In comparison to the mathematical model, the proposed finite element model (FEM) presetting the attachment errors shows the effect of modal vibration and the variation of radial throw with attachment errors. To further investigate the environmental factors influencing the radial throw, a measurement method based on the laser measurement system is presented to achieve the on-machine measurement of runout, and a specific extraction method of attachment errors was proposed to help validate the mathematical model. The difference between the results of the mathematical model, FEM, and the experiment is not exceeding 10 % within 3 μm of the maximum runout. Radial throw varies strongly with attachment errors, and the high rotation speed will aggravate the system instability caused by the attachment errors. The main contributor among experimental factors to the variation of runout is the form accuracy of micro milling cutters, accounting for 4.7 % at the highest. This method can provide a theoretical basis for the sources of unbalanced cutting force analysis and the improvement of dimensional/form accuracy.

An improved FSDT with an efficient mesh-free approach for nonlinear static analysis of FG-GOPRC beams

The aim of this paper is to enhance the First Shear Deformation Theory (FSDT) beam and apply it to investigate the linear and nonlinear static bending behavior of beams containing functionally graded graphene oxide powder-reinforced composite (FG-GOPRC). In this study, we propose an improvement to the FSDT by utilizing a high-order mesh-free approach. Unlike some existing FSDT methods, our proposed study uses a nonlinear shear deformation term coupling, which is crucial to illustrate the effect of nonlinear cases of various boundary conditions under a strong formulation, even without selective or reduced integration, resulting in lower computation costs. Using the principle of minimum potential energy, the governing equations are rewritten in a matrix–vector strong form and discretized using the Radial Point Interpolation Method with variable shape parameter (VS-RPIM) and linearized using a High Order Path Following Techniques (HOPFT). To account for the behavior of GOPRC, we utilized the modified Halpin–Tsai model to estimate the effective Young’s modulus, while the rule of mixture was employed to determine the effective Poisson’s ratio. Furthermore, the weight fractions of the graphene oxide powder (GOP) vary continuously through the thickness direction of the composite beams. To validate the proposed numerical model, we provide various comparison studies to demonstrate its robustness and accuracy. Additionally, we conduct parametric studies to examine the effects of different parameters, such as length-to-thickness ratio, GOP distribution patterns, weight fraction, and size of GOP, types of loads, and boundary conditions on the nonlinear bending behavior of FG-GOPRC beams. We also investigate the neglected term in some literature, which is of interest in our study. In summary, this paper proposes an enhanced FSDT to investigate the nonlinear static behavior of FG-GOPRC beams. The proposed model is validated through various comparison studies and parametric analyses, demonstrating its robustness and accuracy. Our study provides useful insights into the nonlinear bending behavior of FG-GOPRC beams and highlights the importance of nonlinear shear deformation term coupling.

Design of a two-stage compliant asymmetric piezoelectrically actuated microgripper with parasitic motion compensation

The parasitic motion of microgripper jaws affect clamping accuracy. The parallelogram mechanism (PM) is often used as the last-stage of the multi-stage amplification mechanisms (AMs) because of its parallel clamping characteristics. However, the PM traditionally used in multi-stage AMs is asymmetrically stressed, which will affect its parallel clamping accuracy. Based on this, a PM with symmetrical forces is designed. The paper addresses the issue of parasitic motion in microgripper jaws and its impact on clamping accuracy, which is a relevant concern in micro-scale manipulation systems. The design of a symmetrically stressed PM for use in a two-stage asymmetric microgripper is a novel contribution to the field. Based on the minimum potential energy principle and the Castigliano's second theorem, the mechanical modeling of the mechanism's parasitic displacement, magnification and parallel clamping accuracy is carried out. Comparing the mechanical model, finite element analysis (FEA) and experimental measurement results, the values given by the three different methods are close. The method given in this paper to improve the clamping accuracy of the mechanism is also applicable to similar compliant mechanisms.

Torsional Dynamics of Axially Graded Viscoelastic Carbon Nanotubes

Torsional vibration analysis of the axially functionally graded carbon nanotubes has been carried out. Nonlocal stress gradient elasticity theory has been used in continuum mechanics model of the carbon nanotube. Variation of the material properties of the axially graded nanostructure has been assumed in exponential form. Differently from the majority of literature works, viscous damping and nonlocal parameters have been assumed in grading form. Energy functional for the carbon nanotube has been achieved with minimum potential energy principle and weak form solution has been obtained with the Ritz Method. Effects of material grading, nonlocality and viscoelasticity to the torsional dynamics of axially graded carbon nanotube have been investigated. Results of the present work could be useful in modeling and production of axially functionally graded nanostructures.

Nonlinear electromechanical bending of bi-modular piezoelectric laminated beams

In this paper, the nonlinear electromechanical bending of a bi-modular piezoelectric laminated beam is studied based on the principle of minimum potential energy and the Adomian decomposition method. The different tensile-compressive Young’s modulus of the core and piezoelectric layers, and the different tensile-compressive piezoelectric coefficients are considered. The electromechanical governing equations and related boundary conditions are obtained by using the principle of minimum potential energy. The deflection, neutral layer and interlaminar stresses of the beam are solved by the Adomian decomposition method and the iterative method, and verified by the finite element model and Galerkin's method. Results show that the applied voltage and the bi-modular characteristics affect the position of the neutral layer and the interlaminar stresses. Compared with the bi-modular properties of the core layer, the influences of the bi-modular properties of the piezoelectric layer on the neutral layer are relatively unobvious. In addition, the interlaminar stresses between the piezoelectric layer and core layer can be increased or decreased, depending on the relative magnitude of the applied voltage ratio and the bi-modular ratio. The results obtained are helpful for the analysis of the electromechanical coupling mechanism and design of piezoelectric composites and structures with bi-modular characteristics.

Dynamic behavior of risers under nonlinear oceanic environmental loading

The riser system acts as the vital link between the subsea blow-out preventer and the drilling platform. Affected by factors like top tension and marine environmental forces, the riser undergoes deformation and wear, carrying the risk of environmental pollution and financial losses upon failure. Hence, this study examines the riser's dynamic response to marine environmental loading. Initially, the motion differential equation for the riser system under the influence of nonlinear oceanic load is deduced using the principle of minimum potential energy and the variational method for extremum seeking. Subsequently, a nonlinear wave-current load model based on the Morrison equation is established, and the resulting equation is discretized into a finite element model using third-order Hermite interpolation function and the Galerkin weighted residual method. Finally, the dynamic response of the riser is scrutinized employing the Newmark numerical integration method. The study also investigates the impact of both oceanic environmental parameters and drilling parameters on the riser’s dynamic behavior. Comparative analysis of the numerical results reveals that the maximum displacement of the riser occurs at the middle section, whereas the maximum deflection angle is observed at the end of the riser. The periodicity of the deflection angle response is influenced by the position of the riser, showing a trend of decreasing and then increasing from the middle section towards the ends. Notably, the top tension and the velocity of the surface tidal current significantly affect the dynamic behavior of the riser. The findings of this study provide a theoretical foundation for the assessment of riser reliability and the determination of operational parameters.

Exact solution of thermal postbuckling of porous piezoelectric nanobeams with surface effect

In this paper, the thermal postbuckling of porous piezoelectric nanobeams is analyzed using the first-order shear deformation beam theory based on the surface elasticity theory and "core-shell" model, where the surface effect is introduced by employing the surface energy model. The governing equations for thermal postbuckling of porous piezoelectric nanobeams were derived by the principle of minimum potential energy. It is found that surface effect increases the effective elastic modulus and dimensionless critical load and reduces the thermal postbuckling conformations, thermal postbuckling paths and amount of induced charge. Meanwhile, the reasonable pore distribution pattern can effectively improve the mechanical properties.

Application of modified first order shear deformation theory to vibration analysis of SSSS and CCSS thick anisotropic rectangular plates

This research presents a vibration analysis of a thick anisotropic rectangular plate using modified first shear deformation theory. Modified first shear deformation theory, which is not built upon the classical plate theory, was used to develop the kinematic equations and constitutive relations of a deformed section of thick anisotropic rectangular plate from which the generalized stress equations were determined. Using the assumptions of the theory, the strain energy and external work equations were formulated, and by employing the principles of total minimum potential energy, the total potential energy functional of a thick anisotropic plate was developed. Minimization of the total potential energy functional with respect to the deflection function (w) and with respect to the shear rotations (Φx) and (Φy) respectively, resulted in the governing differential equation and the two compatibility equations of the plate. The displacement functions that satisfy the governing and compatibility equations were obtained by solving the governing and compatibility equations. From the general displacement function, the peculiar deflection equations (shape functions) were obtained for the boundary conditions considered, which are simply supported on its four edges (SSSS), clamped on two adjacent edges, and simply supported on the other two (CCSS). Using the displacement equation and the equation for rotation in the x-direction (Φx) and equation for rotation in y-direction (Φy) the direct governing and two direct compatibility equations were obtained, from which coefficients that enable the formula for calculating fundamental natural frequencies to be obtained. For the boundary condition analyzed in this work, the stiffness coefficients (kR, kQ, kRQ, kq, kRRQ , kRQQ , kNR, kNQ, kNRQ and kλ ) were computed and used in determining the fundamental natural frequency parameter values at various span to depth ratios (5,10,20, 25 and 100), aspect ratios (1 to 2 at the increment of 0.1) and angle of fibre orientation (0o, 15o, 45o). The solutions of this study were compared with those from previous researchers. The fundamental natural frequency parameter values obtained in this study were compared with the work of Reddy (1984) for 0o angle of fibre orientation at span to depth ratios of 5,10, 20, 25, 50 and 100 at an aspect ratio of 1. The percentage difference values were 6.073%, 3.197%, 1.132%, 0.788%, 0.255%, and 0.112%, respectively. These differences revealed the closeness of the results of this present study to the results of Reddy (1984). This shows that the present theory provides good and acceptable solutions to the vibration problems of thick anisotropic rectangular plates.

Electro-Mechanical Buckling of Shallow Segments of Functionally Graded Porous Toroidal Shell Covered by Piezoelectric Actuators

The current work deals with the mechanical buckling behavior of saturated porous toroidal shell segments sandwiched by piezoelectric actuator layers. Material properties of the porous shells with nonuniform distributed porosities are assumed to vary as a specific function of the thickness and porosity parameters. The nonlinear equations of the sandwich toroidal shell having either positive or negative Gaussian curvature are obtained on the basis of Biot’s poroelasticity theory. The energy method as the minimum potential energy principle is applied to derive the governing equations of the sandwich shells. The buckling equations of the piezo-porous sandwich shells under various types of mechanical loading are established by employing the adjacent equilibrium criterion. The governing equations as a set of the coupled partial differential equations are solved using an analytical method including the Airy stress function. Closed-form solutions are derived for shallow segments of the sandwich toroidal shell with positive/negative Gaussian curvature under lateral pressure, axial compression, and hydrostatic pressure loadings. Novel numerical results are presented in this work to show the effects of important factors such as the piezoelectric layer thickness, applied voltage, shell geometrical ratio, and variation of the porosity coefficient on the buckling behavior of these structures.

Refined beam finite element model for thin-walled multi-cell box girders considering distortion and secondary distortional moment deformation effect

In this paper, a novel one-dimensional refined beam finite element model (FEM) accounting for non-uniform distortional warping and secondary distortional moment deformation effect (SDMDE) is formulated for the distortional analysis of thin-walled multi-cell box girders with cantilevered flanges. The extra distortional angle is introduced to incorporate SDMDE, and the validity of which is proved through rigorous theoretical derivation. The in-plane and out-plane deformations at any point around the edge of transverse section built upon the distortional center are unified in the same form and described in detail. The governing differential equations in terms of two generalized displacements, distortional angle χ and primary distortional angle curvature Θ, are derived based on the principle of minimum potential energy (MPE) and solved exactly so as to provide non-polynomial shape functions for the establishment of element stiffness matrix and nodal load vector. A series of multi-cell rectangular hollow section (RHS) girders are analyzed and particular extensions are given to single-cell and multi-cell bridge girders with cantilevered flanges. Comparisons to the results generated from corresponding ones provided by pioneering work or shell FEM analyses not only validate the correctness and reliability of the present beam element formulations but also highlight the significance of the inclusion of SDMDE when the cantilevered flanges are arranged.