Plate Finite Element Research Articles

Simulating flow-induced reconfiguration by coupling corotational plate finite elements with a simplified pressure drag

Simulating flow-induced reconfiguration by coupling corotational plate finite elements with a simplified pressure drag

Nonlinear Dynamic Analysis Framework for Slender Structures Using the Modal Rotation Method

Abstract Owing to their low induced drag, high-aspect-ratio wings are often applied to aircraft, particularly high-altitude long-endurance aircraft. An analytical method that considers geometrical nonlinearity is necessary for the analysis of high-aspect-ratio wings as they tend to undergo large deformations. Nonlinear shell/plate or solid finite element methods are widely used for the static analysis of wing strength. However, an increase in the number of elements drastically increases the computational costs of nonlinear finite element methods owing to the complexity of wing shapes. The modal rotation method (MRM) can avoid this additional expense by analyzing large deformations based on modes and stiffness matrices obtained from any linear or linearized model. However, MRM has only been formulated as a static analysis method. In this study, a novel modal-based dynamic analysis framework, referred to as dynamic MRM (DMRM), is developed to analyze slender cantilever structures. This paper proposes a method to discretize dynamics by capitalizing on the fact that MRM considers geometrical nonlinearity based on deformed shapes. Additionally, a formulation method for the work performed by an external force modeled as a follower force is proposed. The energy stored in the structure was consistent with the work performed by an external force in each performed simulation. The proposed DMRM selects the modes used for analyses and systematically determines a time step according to the modes. DMRM achieved a 95% reduction in the calculation time compared with a nonlinear plate finite element method in a performed simulation.

NUMERICAL STUDIES OF THE DISTRIBUTION CAPACITY AND DEFORMABILITY OF THE SPATIAL MODEL OF THE SOIL BASE IN THE FORM OF A LINEAR-DEFORMED LAYER

The article analyses the existing approaches to modelling the interaction between a structure and a soil foundation, which consider the joint deformation of the soil and the structure. The “base-foundation-structure” models can be created in one-dimensional, two-dimensional, or three-dimensional space. Each of these models has its own set of boundary conditions and calculation methodology The advantages and disadvantages of each model, during application in engineering calculations, are presented. The purpose of research is to substantiate the methodology for assigning the geometric parameters of a three-dimensional model of a soil foundation, represented as a linearly deformed layer of finite resolution, for adequate modelling of interaction in the "base- foundation-structure" system. A finite-element model of the interaction between the soil base and the slab foundation was built using the modern SCAD software package. The modelling was performed in three dimensions. The soil base is represented by volumetric finite elements with constant deformation characteristics. The foundation is modelled by plate finite elements In context of this research, the slab model of the foundation was assumed to be rigid to neglect stress redistribution in the above-ground part of the building. Based on the analysis of modern approaches to the assignment of geometric parameters to the model of the soil base represented by a continuous linearly deformed layer with finite overall dimensions, which is created in a three-dimensional problem statement, it was shown that today there is no single approach to modelling such a “base-foundation-structure” system. Numerical studies of the effect of rigid horizontal constraints in the plan on the stress-strain state of a uniformly loaded rigid foundation interacting with a linearly deformed layer (compressible thickness) of finite distribution capacity were carried out using the SCAD program. Based on the analysis of the results of numerical calculations for a three-dimensional problem, the minimum allowable sizes in terms of the model of a linearly deformed layer of finite distribution capacity, which considers the distribution of compressive stresses along the depth at an angle of α = 25º to the vertical from the edges of the loaded foundation, are substantiated. At the same time, the overall size of the model in the plan according to the distribution angle α = 25º has practically no effect on the average settlement and maximum moment forces of the foundation compared to the angle α = 45º. Keywords: slab foundation, soil foundation, linear-deformed model, distribution angle, stress-strain state.

The Q4γs plate finite element for three-layer FGM sandwich plates in deflection, stresses, vibration, and thermal buckling analysis

This work adapts the Q4γs quadrilateral element to analyse three-layer FGM sandwich plates. Two types of FGM sandwich configurations are employed to assess the element performance in conducting static, free vibration, and thermal buckling analysis. The first configuration is a homogeneous core and FGM outer layers, while the second involves homogeneous top and bottom layers and an FGM core. Various problems have been run, and the results are compared with references to assess the accuracy of the element. Numerical results on the deflection, stresses, frequencies, and thermal buckling of symmetrical and non-symmetrical FGM sandwich plates are examined to evaluate the effectiveness of the current model. Furthermore, the influence of the power-law index and the length-to-thickness ratio on the analyses is also investigated.

Three-node Mindlin plate finite element with shear stress resultants derived from equilibrium equations

Three-node Mindlin plate finite element with shear stress resultants derived from equilibrium equations

An efficient shear and bending‐locking‐free quadrilateral plate element using a modified Hellinger‐Reissner functional and the Bergan free formulation

AbstractThis paper presents a general variational principle as theoretical support for creating a simple and efficient quadrilateral plate finite element called BKWA, having only a single displacement and two rotations at corner nodes according to the Reissner‐Mindlin plate theory. The functional is a modified Hellinger‐Reissner in terms of the kinematic variables and independent transverse shear strains. Hence, we consider quadratic rotations, as in DKQ, and linear independent shear strains with constant tangential components on sides, as in MITC4. The quadratic rotation contributions and the mixed shear strain components are wiped out by static condensation. To adequately satisfy the constant curvature patch tests, we also consider the orthogonality conditions between the linear and quadratic bending modes, as in the Bergan free formulation, to avoid ‘spurious bending energy’ for thick plates (also called bending locking). The paper contains comprehensive patch tests and convergence tests with regular and irregular meshes (displacements, internal forces, and strain energy) of circular and square plates. The element is compared with other existing elements (MITC4, DKMQ). It is concluded that BKWA is an efficient element regarding several criteria.

Enhanced beam and plate finite elements with shear stress continuity for compressible sandwich structures

This paper concerns and presents new improved beam and plate finite elements for analysing sandwich structures from the structural and modal points of view. In this study, the material behaviour is supposed to be linear elastic and orthotropic, but the method could be extended for nonlinear problems as well. The current models are able to treat the compressibility of the soft core materials, besides the interlaminar continuity conditions and the zero shear stresses on the shear-free surfaces are granted by the Lagrange multiplier method. In order to provide stress continuity along the element boundaries, the Hermite interpolation is employed for the elementary formulations that yields subparametric finite elements. On the contrary, the semi-analytical solutions of these enhanced beam and plate models are also discussed here for particular boundary conditions. The verification of the new finite elements is carried out by two case studies. The test examples are modelled and solved in commercial finite element software (ANSYS) with general shell and solid elements, too. The results derived from different models are subjected to a comprehensive comparison. Also, the structural and modal analyses of the test examples are presented during the case studies. The structural analysis of an overconstrained sandwich panel is also discussed to point out the significance of the proper shear stress distributions. Finally, the advantages and disadvantages of the newly developed elements and semi-analytical solutions are revealed in detail.

Uticaj temperaturskog gradijenta na savijanje tankih ploča

Within the theory of thermo-elasticity, the temperature field of thin plates is commonly defined via two parameters: temperature in the mid-plane and linear temperature gradient normal to the mid-plane. First, the paper analytically proves the justification of that assumption in machine structures. Then, in an analytical closed form, applying the integral transformation method, the thin plate deflection caused by a constant temperature gradient is defined. It is shown that, in that case, the plate deflection does not depend on its thickness but only on the plate dimensions in the mid-plane. Analytically defined values are compared to corresponding values obtained by applying the thin plate finite element, where the temperature field is described using the two mentioned parameters. This finite element is defined and programmed within the Komips program package. The influence of the temperature gradient on the behavior of constructions mostly depends on the type of material. That is why the behavior of some structural elements made of brass, steel, and concrete is analyzed in this paper.

Analysis and experimental verification of dynamic characteristics of cantilever plate with fatigue crack

Fatigue cracks in aero-engine blades seriously threaten the stability and reliability of the engine. It is very necessary to identify and diagnose the crack state through vibration signals, and predicting its vibration rules through dynamic analysis is the basis of crack identification. At present, the dynamic model of cracked blades with breathing cracks is mainly established by implanting cracks, and there is a lack of relevant experimental validation. To address the above deficiencies, this paper firstly obtains the real extension path of the cracked plate through the fatigue testing machine, and then introduces it into the cantilever plate finite element model. Then the correctness of the proposed model is verified by natural frequency obtained from hammering test and frequency sweeping test. Finally, the effect of different crack parameters such as crack depth, crack location and plate length on the crack vibration characteristics is investigated based on simulations and experiments. The results indicate that (1) the real fatigue crack obtained by tensile test has larger amplitude peaks under excitation frequency compared with wire-cut crack, and it has stronger nonlinearity to better reflect the vibration characteristics; (2) Specimens show obvious nonlinear characteristics that significant amplitude peaks occur at multiples of excitation frequencies in both experiments and simulations; (3) For the cantilever plate containing breathing cracks, the vibration amplitude totally increased by 18.5% with the increase of crack depth, and it decreased by 41.5% throughout as the crack location became further away from the plate root. This study provides a theoretical basis for detection and diagnosis of blade cracks.

Variable kinematics finite plate elements for the buckling analysis of sandwich composite panels

This paper extends sublaminate-based variable kinematics plate finite elements towards the buckling analysis of composite structures. Robust locking-free 4-node and 8-node interpolations are used to build the finite element matrices in terms of fundamental nuclei, invariant with respect to the employed kinematic model of the composite plate. Geometric nonlinearities are accounted for in the von Kármán sense. The classical linearized stability analysis is mainly conducted for sandwich panels, for which different kinematic assumptions are employed for the skins and the core. Global buckling of the sandwich panel as well as short-wavelength wrinkling of the skins are investigated by referring to a variety of case studies, including homogeneous and laminated skins as well as isotropic and orthotropic cores. Convergence studies are performed to establish the minimum number of elements for the local instabilities to be grasped. The proposed computational framework requires a simple 2D mesh and is capable of providing quasi-3D response patterns. This is as demonstrated by numerous case studies that address the transition from global to local buckling, the onset of wrinkling in flat sandwich panels with anisotropic skins under various loading conditions as well as the local face sheet instability occurring in sandwich panels working in bending. It is concluded that he proposed FEM-based tool is computationally efficient and can be advantageously employed in pre-sizing design phases without resorting to full 3D models.

A unified buckling formulation for linear and nonlinear analysis of laminated plates using penalty based [formula omitted] FEM-HSDT model

In this paper, the effect of pre-buckling boundary conditions and the type of nonlinearity for stress stiffening used in different linear and nonlinear buckling approaches is studied for laminated composite plates. The study is conducted using a C0 finite element (FE) plate model, employing a unified C1 higher-order shear deformation theory (HSDT). The set of governing equations is derived using the principle of virtual displacement and solved using the tangent-based arc-length method in conjunction with a simple branch switching technique. The performance of the present C0 FE model is assessed through a validation exercise and comparison with results obtained via the use of ANSYS and, for linear analysis, Navier solution, as well as solutions available in the literature. The influence of the different in-plane loads, boundary conditions, side-to-thickness ratio, fiber orientation, types of imperfection and penalty stiffness matrix are also examined. The results show that the same boundary conditions must be utilized in both pre-buckling and linear eigenvalue analyses for accurate and realistic predictions of critical buckling loads, as confirmed from the nonlinear buckling analyses. Furthermore, the critical buckling loads obtained using Green–Lagrange nonlinearity are observed to be more conservative than those obtained using von Kármán nonlinearity. The nonlinear buckling approach is a generalized approach while the nonlinear eigenvalue approach has a limited range of application.

Influence of Initial Structural Dimensions of Plates on Welding Distortion

Aiming at the complex full-field deformation problem that easily occurs when welding plates, this paper adopts the elastic–plastic finite element method with heat-force coupling to study the deformation law of plates in different initial states. First, a rectangular plate finite element model with an initial radius and Gaussian heat source model was established to obtain the welding temperature field and deformation field of the plate; then, the method based on digital image correlation technology was used to detect the full-field dynamic deformation of the plate to verify the accuracy of the finite element model; finally, the influence of the initial structural dimensions of the plate on the weld deformation was investigated. The study shows the following: the thermoelastic–plastic finite element model proposed in this paper has high accuracy in both static and dynamic deformation; plates with the same curvature, and different lengths and widths of the initial structure of the plate welding deformation are saddle-shaped, and the edge effect of the welding of the plate is evident, independent of the length of the plate; and the maximum out-of-face deformation of the welding of the plate is linearly related to the length and the closer the aspect ratio of the plate is to 1, the smaller the out-of-face deformation is.

Конечно-элементная модель перегрузочного крана КПП 16/32т для перевалки грузов в речных и морских портах

Transshipment cranes of the checkpoint of the Lenpodyemtransmash plant are widely used in river and sea ports, at industrial enterprises for grappling transshipment of bulk cargo and for working with piece loads or containers, as well as for transshipment of scrap metal and rolled metal using lifting electromagnets. It is proposed to eliminate the uncertainties caused by the incompatibility of one-dimensional (rod) and two-dimensional (plate) finite elements having a different number of degrees of freedom, 12 and 20, when developing digital twins of portal cranes of the Lenpodyemtransmash plant on the example of the CHECKPOINT 16/32t crane by approximating axisymmetric shells of the portal head with rod finite elements. The method is based on the equality of the potential shear energy of the finite element model of the plate and the potential energy of the approximating rod model, the elements of which work on tension/compression, which made it possible to move from the finite element model of the GEARBOX 16/32t reloading crane, built on the basic finite elements of Kirchhoff plates, to the finite element model of the crane based on the core base finite elements. A mathematical model of a matrix equation of static equilibrium with many degrees of freedom is proposed, the numerical solution of which by the Gauss method allows us to proceed to six-component internal forces in each finite element due to the corresponding vector of external loads reduced to the degrees of freedom of the calculated finite element model. The possibility of inter-pretation of bearing elements of spatial metal structures of portal cranes by both one-dimensional rod and two-dimensional plate finite elements is investigated, a re-evaluation of traditional views on the computational analysis of the stress-strain state of metal structures of portal cranes in the field of reliable determination of their bearing capacity during operation in ports, especially in the field of assessing post-repair risk analysis and the resource of reloading cranes is proposed, those who have completed the standard service life in the port and have undergone capital repairs. A calculated rod finite element idealized model of a PPC 16/32t gantry crane for transshipment of cargo in river and sea ports is constructed, demonstrating the transition from a real design to a calculation model based on geometric principles of discretization of both rod and continuum elements by the basic rod end elements of the crane, as a result of which the digital calculation model should be detailed and complex, like a system with many degrees of freedom. The algorithm of application of the digital calculation model of the crane is given on the example of static finite element calculation analysis of the KPP 16/32t crane.

A numerical study of the multicriteria parametric optimization of the displacement and weight of a two-connected conical shell of minimal surface under thermal and power loading

Various methods and approaches are used to solve the problem of optimal design. Problems of this type are used for the optimal design of spatial coverings, which in modern architecture are progressive structures that are of interest to the whole world. Spatial coatings allow to give the building architectural expressiveness, cover large spans and combine load-bearing and enclosing functions.
 The hulls of minimal surfaces are the hulls of negative Gaussian curvature. In general, the geometry of minimal surfaces cannot be described analytically. To solve this problem, which is associated with solving the differential equation that describes the minimal surface in general, under appropriate boundary conditions, one has to use methods of numerical analysis. This approach allows us to build a point frame of the shell, which is a matrix of discrete solutions of functions that searches for a given minimum surface. In view of this, its geometric characteristics can be obtained only in numerical form.
 The basic relations of the linear theory of thin elastic shells of minimal surface are highlighted in the numerical study of parametric optimization. The mathematical justifications of how the external load is perceived and the process of creating the stress-strain state of the shells of minimal surfaces are highlighted.
 For the numerical implementation of the multicriteria parametric optimization of a double-connected conical shell of minimal surface, a finite element model was built from plate finite elements in the amount of 4824 pieces and 4896 nodes. The perimeter is rigidly clamped to the ground disk. The thermal force load is set, which consists of a combination of static and temperature loads.
 The developed methodology shows quite good results that coincide with the works of other authors and makes it possible to use two types of optimization for one research object simultaneously. The first stage is shape optimization, and the second stage is multicriteria parametric optimization.
 This methodology makes it possible to perform optimization processes in an automated mode, which is an important applied task for construction and applied mechanics.

Advanced finite element analyses to compute the J-integral for delaminated composite plates

This study concerns several possible ways of computing the J-integral in the cases of laminated composite plate structures containing delamination. On the one hand, two special types of plate finite element families are provided for advanced fracture mechanical analyses. On the other hand, a numerical algorithm is introduced also that utilizes results derived from solid element models built in commercial finite element software. In order to create plate elements, the first-order (FSDT) and the third-order shear deformation theories (TSDT) are applied with two equivalent single layers. A subparametric element family is created by using the Hermite interpolation with the FSDT that grants the continuity of the derivatives at the element borders. Besides, an isoparametric family is created also with the TSDT employing the Lagrange interpolation scheme. This paper aims to present the compact formulations of calculating the J-integral around the delamination fronts for both plate element families. The calculation of the J-integral is implemented as a matrix multiplication by taking advantage of the properties of plate transition elements. The models yield improved fracture mechanical analyses for delaminated composite plates with linear elastic material behaviour. In addition, computing the J-integral is not available in most commercial finite element software for laminated orthotropic materials, therefore, an appropriate algorithm is presented here for this purpose. To conclude, the models and algorithms are applied to two case studies and subjected to a comprehensive comparison with analytical and formerly used finite element solutions.

A mechanical analysis of variable angle-tow composite plates through variable kinematics models based on Carrera’s unified formulation

Variable Angle-Tow (VAT) laminates offer a promising alternative to straight fiber composites. By varying fibers orientation within the structure plane, ambitious design and performance goals can be achieved. However, the wider design space results in a more complex problem with more parameters to consider. Carrera’s Unified Formulation (CUF) has been used in previous works performing buckling, vibrational and stress analyses of VAT plates. Usually, one-dimensional (1D) CUF beam models are used, while two-dimensional (2D) plate models are obtained as a particular case of shells by considering a null curvature. In most cases, a linear law is considered to describe the variation of fibers orientation in the main plane of the structure. The purpose of this article is to extend the CUF 2D plate finite elements family to the mechanical analysis of composite laminated plate structures with curvilinear fibers. The main contribute consists in the development of a CUF FE model within the Reissner’s Mixed Variational Theorem (RMVT) context for an improved calculation of the out-of-plane stress components. Results show that RMVT can predict in-plane stresses and satisfy the though-the-thickness transverse stresses continuity due to inter-layer equilibrium. The accuracy of RMVT-based models is also investigated using two different approximation points distributions along the plates thickness.

Thermal stress analysis of variable angle tow composite plates through high-order structural models

This work focuses on thermo-elastic analysis of Variable Angle Tow (VAT) composite plates. Emphasis is given to the through-the-thickness 3D stress component distributions as a consequence of constant temperature profiles. High-order structural models are used, in order to take into account the volumetric and the distortion contributions. The last contribute arise from boundary conditions or asymmetric staking sequences. Governing equations of the uncoupled thermo-elastic problem are derived in the domain of the Carrera Unified Formulation (CUF), which in turn is coupled with a classical finite element method to obtain opportune numerical solutions. The advantage of using CUF lies in the fact that different theories of structures can be implemented automatically and a critical study on the use of standard to high-order plate finite elements can be performed with ease. In this manner we classify models based on their efficiency and depending on the degree of accuracy needed, both in terms of displacements and stresses. Different numerical problems are considered and it is demonstrated that layerwise approximations are needed whenever shear stresses trends are of interest. Boundary Conditions influence more the choice of the adequate expansion theory otherwise.

Analysis of transversely isotropic compressible and nearly-incompressible soft material structures by high order unified finite elements

This work proposes high-order beam (1D) and plate (2D) finite element models for the large strain analysis of compressible and incompressible transversely isotropic hyperelastic media, defined within the Carrera Unified Formulation (CUF) framework. The strain energy density function adopted in fiber-reinforced hyperelastic materials modeling is presented and expressed in terms of invariants and pseudo-invariants of the right Cauchy-Green strain tensor. The explicit expression of the tangent elasticity tensor is derived through the assumption of coupled formulation of strain energy functions. Refined fully nonlinear beam and plate models are defined in a total Lagrangian formulation, deriving the governing equations of the nonlinear static analysis through the Principle of Virtual Displacements in terms of fundamental nuclei, in resulting expressions of internal and external forces vectors, and tangent stiffness matrix independent of kinematic models and approximation theories adopted. The iterative Newton-Raphson linearization scheme coupled with the arc-length constraint is adopted to obtain actual numerical solutions. Different benchmark analyses in hyperelasticity are performed to assess the capabilities of our proposed model, analyzing the three-dimensional stress field for moderate to large strain states and comparing actual numerical results with exact closed-form solutions or results available in the literature, demonstrating the capabilities and reliability of CUF models in the analysis of fiber-reinforced soft materials and structures.

A four-node rectangular plate finite element using Airy functions with transverse shear

PurposeAmong different types of engineering structures, plates play a significant role. Their analysis necessitates numerical modeling with finite elements, such as triangular, quadrangular or sector plate elements, owing to the intricate geometrical shapes and applied loads. The scope of this study is the development of a new rectangular finite element for thin plate bending based on the strain approach using Airy's function. It is called a rectangular plate finite element using Airy function (RPFEUAF) and has four nodes. Each node had three degrees of freedom: one transverse displacement (w) and two normal rotations (x, y).Design/methodology/approachEquilibrium conditions are used to generate the interpolation functions for the fields of strain, displacements and stresses. The evolution of the Airy function solutions yielded the selection of these polynomial bi-harmonic functions. The variational principle and the analytical integration approach are used to evaluate the basic stiffness matrix.FindingsThe numerical findings for thin plates quickly approach the Kirchhoff solution. The results obtained are compared to the analytical solution based on Kirchhoff theory.Originality/valueThe efficiency of the strain based approach using Airy's function is confirmed, and the robustness of the presented element RPFEUAF is demonstrated. Because of this, the current element is more reliable, better suited for computations and especially intriguing for modeling this kind of structure.

A finite element for static and dynamic analyses of cross-laminated timber floors

In this paper, a finite plate element for floorings consisting of a cross-laminated timber slab and a floating floor based on linear elastic behavior is presented. Both elemental mass and stiffness matrices are derived, allowing for static and dynamic analyses. For the cross-laminated timber plate, a higher order plate theory is employed, capturing the layer-wise zig-zag deformation of the plate and the stresses derived thereof accurately. It is augmented by an elastic layer representing the footfall sound insulation and an isotropic plate modeling the screed of a floating floor. In total, the finite element exhibits ten nodal degrees of freedom. Hence, larger structures can be analyzed efficiently, which is demonstrated by comparative finite element simulations with a commercial software package based on continuum elements.