Flat Shell Research Articles

Analysis of the cylindrical shell model using a new four node quadrilateral element compared to ABAQUS elements

Shell models and loadings are very complicated in practice, especially in civil and mechanical engineering, due to their lightweight properties and ability to resist loads. Then; numerical tests are very important for this type of structure. In this work, numerical investigations of a cylindrical shell under concentrated loads are presented. Two finite elements used for this study, the new element ACM-Q4SBE1 and the S4R element of the code “ABAQUS”. The results obtained by the two elements, ACM-Q4SBE1 and S4R ABAQUS, are in agreement. The superiority and efficiency of the flat shell element approach for thin shell structures has been confirmed.

CALCULATION OF FLAT SHELLS BY THE BOUNDARY ELEMENT METHOD

This article describes the iterative process of solving the problem of the stress-strain state of a long flexible cylindrical panel. Stress-strain state and the study of the stability of flat shells taking into account the physical, mechanical properties of the material, the process of deformation change. It is based on sequential approximation methods and the boundary element method (MGE). The results of algorithmic weighting are presented in the form of a table showing what value each band represents. The equations are determined by solving twelve unknown values of functions at the ends of the segment. Linear problems of elasticity theory and plate theory fundamental solutions have a simple form, so the method is widely used here. For flat shells, the matrix of fundamental solutions is determined by complex volumetric expressions, and for flat shells - by special functions. Therefore, there is little research on solving problems in the theory of flat shells by the boundary element method. In this regard, an urgent topic of research is the development of methods of boundary integral equations for solving linear and nonlinear problems in the theory of flat shells based on the application of fundamental solutions defined by simple analytical expressions. The scientific novelty of the work consists in the development of a methodology for assessing the reliability of thin-walled spatial structures using the boundary element method.

Development of nonlinear flat shell element with nonlinear thickness variation for highly flexible wind turbine blade

Large deformation from continuously varied thicknesses on existing and wind turbine blade shell structures is investigated. Various structure models having complicated outer shapes and thickness variations are considered and validated in this paper. A co-rotational method is developed to analyze geometric nonlinearity with a triangular shell structure. The updated stiffness matrix from interpolated thickness function and integral formulation is suggested to consider complicated geometry and thickness variation. Moreover, the co-rotational flat shell element based on the updated stiffness matrix is developed to analyze various nonlinear shell structures, which are the main feature of this research. The numerical analysis for structure deformations show well matched trends in static load analysis. Furthermore, the deformation of a simplified flexible wind turbine blade having tapered geometry and various thickness cases is adopted as a practical case. Moreover, modal analysis for composite beam structure is performed to verify the dynamic problems. The structural behaviors of the nonlinear thickness shell are validated against the solid and the shell models in commercial software, ABAQUS.

Geometrically nonlinear analysis of plates and shells by a cell-based smoothed CS-MITC18+ flat shell element with drilling degrees of freedom

A development of a 3-node triangular flat shell element to analyze geometric nonlinearity of plate and shell structures is presented in this study. The proposed flat shell element has 6 degrees of freedom per node, including the drilling rotational ones, by using the Allman-type approximations for the in-plane displacements and the bending displacement approximations enriched by a cubic shape function at the bubble node located at the element's centroid. The geometrically nonlinear behaviors are described by the von Karman's large deflection assumption. The membrane and bending strains of the presented flat shell elements are averaged over sub-triangular elements based on the cell-based smoothed (CS) technique. To attenuate the shear locking phenomenon, the transverse shear strains are re-interpolated following the mixed interpolation of tensorial components (MITC) technique designed for the 3-node triangular degenerated shell elements enriched by a cubic bubble function (MITC3+). Combined with the Newton-Raphson iterations and load increments predicted by the arc-length method, the suggested 3-node triangular flat shell elements, namely the CS-MITC18+ element, can analyze moderately geometrical nonlinearity, including the snap-thought and snap-back behaviors, of various plates and shells with the different shapes, thickness, and boundaries. The numerical investigations show that the load-displacement curves provided by the CS-MITC18+ flat shell elements well agree with other references.

A CS-MITC18+ flat shell element for static and frequency analyses of laminated composite plate and shell structures

A CS-MITC18+ flat shell element for static and frequency analyses of laminated composite plate and shell structures

Development of Higher Order Stiffened Shell Element (HOST9) for the Static Analysis of Stiffened Laminated Plates

Abstract A new higher order stiffened shell element (HOST9) is developed comprising of a 9 noded flat shell element and a 3 noded stiffener element for analysis of stiffened laminated plates. The shell element is a lagrangian element. The stiffener is a beam element. The stiffness of the stiffener is computed separately and added to that of the shell element at appropriate locations. As a result, the stiffener can be located arbitrarily in the shell element. Static analysis of stiffened laminated plate is carried out using the newly developed element and is validated with the existing literature. It is seen that the proposed element gives comparable results and can be used for the analysis.

Alternative Low-Order Triangular Elements for Thick and Thin Shell Analysis

In this paper, the authors discuss the development of six low-order triangular elements for the linear static analysis of thick and thin shell structures. The elements combine two triangular plane stress elements with three triangular thick plate bending elements to produce three-node flat shell elements with 18 degrees of freedom. The two plane stress components are based on the free formulation and the template formulation, while the three plate bending components are based on the free formulation, the deviatoric strain formulation and the hybrid-Trefftz formulation. The theoretical backgrounds and formulations of all elements are briefly discussed to provide a concise summary, while further details are given in the quoted references. The elements are used to analyze five standard shell benchmark examples, and the results obtained are compared to previous work in this area. The elements provide accurate and robust results for the benchmarks, with only small differences for the results as the meshes are refined. While all the proposed elements can be recommended for general shell analysis, the combination of the template plane stress element and the hybrid-Trefftz plate bending element generally provides the best results.

Shell shape polymorphism analysis of the Manila clam Ruditapes philippinarum across different geographical populations in China

Morphology of bivalves, a kind of quantitative character, is closely connected with the ecological and physiological behaviors of bivalves, including growth, survival, metabolism and reproduction. In this study, a multivariate statistical method was used to analyze seven indices for shell shape evaluation of Ruditaps philippinarum (R. philippinarum). Polymorphism of R. philippinarum shell shape across seven geographical populations from the southern and northern regions of China was revealed, and decisive effect of shell shape in determining the trait of weight was discussed. In total, three types of R. philippinarum shell shape were observed: globular, flat, and lateral-view round. The Laizhou (LZ) population from the north of China displayed an approximately globular shell shape, with a shell-width-to-shell-length ratio of 0.5496 and an ellipse index ventral view (EIV) value of 0.9543. The Lianjiang (LJ) population from the south of China displayed a flat shell shape, with a shell-width-to-shell-length ratio of 0.4044, an ellipse index lateral view (EIL) value of 1.2518, and an EIV value of 0.7063. The Zhangzidao (ZZD) population from the north of China displayed a lateral view round shell shape, with a shell-width-to-shell-length ratio of 0.7476 and a circle index lateral view (CIL) value of 0.7195. According to the results of principal component analysis (PCA), discriminant analysis and cluster analysis on shell shape parameters, LJ population and LZ population could be grouped separately. However, despite the long geographical distance, Rongcheng (RC) population was highly similar with ZZD population in terms of shell shape traits, implying that these two populations might be more closely related. Lowest degree of divergence in shell shape was observed in Beihai (BH) population and Yingkou (YK) population, both of which belonged to Zuidong (ZD) population. Weight of globular Manila clams was significantly higher than that of flat clams (P < 0.05). This study not only lays a foundation for conservation of R. philippinarum germplasm resources, but also highlights the importance of considering shell morphology in the breeding and culture of R. philippinarum.

Free vibration analysis of thin-walled folded structures employing Galerkin-based RKPM and stabilized nodal integration methods

A Galerkin-based meshfree flat shell formulation is chosen to study natural frequency and eigenmode of thin-walled folded structures. Reproducing kernel is used as the interpolation function. Stabilized conforming nodal integration is employed for numerical integration of the weak form. Additionally, sub-domain stabilized conforming integration is adopted for the folded region to integrate the stiffness matrix accurately. The first order shear deformation theory is utilized considering in-plane deformation, out-of-plane deformation and drilling components. The singular kernel function is introduced to effectively handle the folded geometry. An advanced free vibration simulation can be achieved. Accuracy and effectiveness of the meshfree modeling are demonstrated through the numerical examples.

Shell shape does not accurately predict self-righting ability in hatchling freshwater turtles

Flat hydrodynamic shells likely represent an evolutionary trade-off between adaptation to an aquatic lifestyle and the instability of more rounded shells, thought beneficial for self-righting. Trade-offs often result in compromises, this is particularly true when freshwater turtles, with flatter shells, must self-right to avoid the negative effects of inverting. These turtles, theoretically, invest more biomechanical effort to achieve successful and timely self-righting when compared to turtles with rounded carapaces. This increase in effort places these hatchlings in a precarious position; prone to inversion and predation and with shells seemingly maladapted to the act of self-righting. Here, we examine hatchling self-righting performance in three morphologically distinct freshwater turtle species (Apalone spinifera, Chelydra serpentina and Trachemys scripta scripta) that inhabit similar environmental niches. We demonstrate that these hatchlings were capable of rapid self-righting and used considerably less biomechanical effort relative to adult turtles. Despite differences in shell morphology the energetic efficiency of self-righting remained remarkably low and uniform between the three species. Our results confound theoretical predictions of self-righting ability based on shell shape metrics and indicate that other morphological characteristics like neck or tail morphology and shell material properties must be considered to better understand the biomechanical nuances of Testudine self-righting.

Many roads to success: alternative routes to building an economic shell in land snails.

Land snails exhibit an extraordinary variety of shell shapes. The way shells are constructed underlies biological and mechanical constraints that vary across gastropod clades. Here, we quantify shell geometry of the two largest groups, Stylommatophora and Cyclophoroidea, to assess the potential causes for variation in shell shape and its relative frequency. Based on micro-computed tomography scans, we estimate material efficiency through 2D and 3D generalizations of the isoperimetric ratio, quantifying the ratios between area and perimeter of whorl cross-sections (2D) and shell volume and surface (3D), respectively. We find that stylommatophorans optimize material usage through whorl overlap, which may have promoted the diversification of flat-shelled species. Cyclophoroids are bound to a circular cross-section because of their operculum; flat shells are comparatively rare. Both groups show similar solutions for tall shells, where local geometry has a smaller effect because of the double overlap between previous and current whorls. Our results suggest that material efficiency is a driving factor in the selection of shell geometry. Essentially, the evolutionary success of Stylommatophora likely roots in their higher flexibility to produce an economic shell.

Linear composite curvature MITC3+ flat shell elements

This paper introduces a novel linear composite curvature MITC3+ flat shell element, named κMITC3+, that combines the advantages of the MITC3+ theory for flexural (bending and shear) behavior and the Allman-like triangular element (which ensures a true rotation of drilling degrees of freedom and eliminates a spurious energy mode) for membrane behavior. To enhance the bending behavior of the MITC3+ approach, we propose an assumed composite curvature field that is constructed using a polynomial projection technique derived from the orthogonality condition of the compatibility equation in the Hu-Washizu principle. Since two additional internal cross-section rotations are interpolated by cubic bubble functions, a linear polynomial function of the admissible space is chosen that provides a significant enhancement of bending behavior. The κMITC3+ element successfully passes all critical tests and exhibits superior performance compared to the original MITC3+ element and the recent CS-MITC18+ element.

Post-buckling analysis of shell-like structures using an implicit dynamic time integration scheme

PurposeThis paper aims to investigate post-buckling responses of shell-like structures using an implicit conservative-decaying time integration dynamic scheme.Design/methodology/approachIn this work, the authors have proposed the use of a four-node quadrilateral flat shell finite element with drilling rotational degree of freedom within the framework of an updated Lagrangian formulation mutually with an implicit conservative-dissipative time integration dynamic scheme.FindingsSeveral numerical simulations were considered to evaluate the accuracy, robustness, stability and the capacity of the considered time integration scheme to dissipate numerical noise in the presence of high frequencies. The obtained results illustrate a very satisfying performance of the implicit conservative-dissipative direct time integration scheme conjointly with the quadrilateral flat shell finite element with drilling rotation.Originality/valueThe authors have investigated the potential of the implicit dynamic scheme to deal with unstable branches after limit points in the non-linear post-buckling response of shell structures with no need for structural damping. The capability of the studied algorithm to study buckling and post-buckling behaviour of thin shell structures is illustrated through several numerical examples.

Analysis of shell structures by an improved 3-node triangular flat shell element with a bubble function and cell-based strain smoothing

An enhanced 3-node triangular flat shell element with 18 degrees of freedom according to the Reissner–Mindlin theory is presented in this paper. New cell-based smoothed (CS) bending strains were derived from the displacement approximations enriched by a cubic shape function for the rotations at the bubble node located at the centroid of the triangular element. The true drilling degrees of freedom of the proposed element, which is independent from user-defined coefficients, was achieved by cell-based smoothing the Allman’s membrane strains. The membrane and bending stiffness matrices were then efficiently determined by the line integration of the smoothing domains’ boundaries. The shear-locking removal MITC3+ technique was employed to interpolate the transverse shear strains. The outstanding performance of the developed 3-node triangular flat shell element, so-called the CS-MITC18+ shell element, was demonstrated through the static and free vibration analyses of several benchmark shell structures. Numerical results shown that the CS-MITC18+ flat shell element has the spatially isotropic and zero-energy mode properties, and provides competitive accuracy, convergence, and computational cost in comparison to other conventional and strain-smoothed 3-node triangular flat shell elements.

Analytical Modeling of a Membrane-Based Pneumatic Soft Gripper

Finite deformation is the principal actuation basis of elastomer-based pneumatic soft actuators. Desired deformation behavior is the key design requirement for such actuators. The objective of current study is to optimize the design of a flat shell gripper and to investigate its interaction with a cylindrical object. Herein, we propose an analytical model for a membrane-based flat shell gripper. The model is based on finite strain membrane theory and neo-Hookean material. The proposed model considers the contact interaction of the actuator with flat and cylindrical rigid substrates. The model is developed for three different states of the actuator: 1) free-space; 2) contact with a flat substrate; and 3) contact with a cylindrical substrate. In application, the model was used to predict the relative position and air pressure required to grasp a cylindrical object by a parallel two-fingered shell gripper. Additionally, the frictional behavior of the actuator in contact with a cylindrical substrate is investigated. The model involves only solving nonlinear algebraic equations and is computationally efficient. The theoretically predicted deformation behavior of the actuator is experimentally validated via free-space deformation, force measurement, and grasping tests.

Analysis of horizontal silo pressure distribution by filling method based on experimental data

The work presents an analysis of the results of the fill-in condition influence of particle inclination on horizontal silage pressure. Analyzed data were obtained from experiments on a rectangular silo model with rigid walls in a different fill-in condition. The filler was a composite mixture of sand and flat shell particles (2:1). The analysis of the results concluded that the volume weight of the composite mixture depends on the fill-in method, which affects the horizontal silage pressures. At filling of 0° and 45°, the pressure is slightly different from Jansen's theory (max 19%) which can be neglectable. Horizontal silage pressures are functionally dependent on the filling method (up to 44%), which should definitely be taken into account.

Large Displacement Analysis With Material Nonlinear of Shell Structure Using New Flat Shell Elements

In this study, we propose a numerical algorithm for a nonlinear large displacement analysis method using flat shell elements in the hybrid-type penalty method (HPM). First, we describe the flat plate elements of HPM using the local coordinate system. Even with a flat plate, the adjacent elements have an angle at which a large displacement occurs. Next, we propose the relative displacement in this case. The “step-by-step method” is used as the algorithm for material nonlinear analysis and large displacement analysis. Finally, the accuracy of the solution of the proposed method is verified using a simple numerical example.

A four node quadrilateral shell element for free vibration response of functionally graded spherical shell panels

Abstract The present work involves the free vibration analysis of functionally graded spherical shells using a four-node quadrilateral shell element. This four-node, shell element has seven DOF (Degrees of Freedom) per node namely; three displacements, two rotations of mid-plane, and two transverse shear strain com-ponents. The element is developed by modifying the discrete Kirchhoff quadri-lateral shell element based on Reddy’s third-order theory developed earlier by the authors for the cylindrical shell. By transforming all the degrees of freedom from local to global coordinates using a transformation matrix converts the plate bending element into a flat shell element, resulting in the present formulation being suitable to give results for thin shells as well as for thick shells. In the present work functionally graded spherical shell panels with simply supported as well as clamped boundary condition, with various radius to span ratios and with different volume fraction indices are analyzed for free vibration response. The power law property variation through the thickness is considered in this study. To assess the performance of the developed element, the results, of non-dimen-sionalised frequencies are compared with the results presented in the literature. Comparison of results shows that the developed element yields quite accurate results even with the coarser mesh, which indicates the computational efficiency. It is also seen that the percentage difference between the present results and the other results available in the literature is less than 2 in most of the cases.

An edge center based strain-smoothing element with discrete shear gap for the analysis of Reissner–Mindlin shell

In this paper, an edge center based strain-smoothing element with discrete shear gap method (ECSSE-DSG) based on triangular Reissner–Mindlin flat shell element is proposed to solve shell problems. In the proposed ECSSE, the strains for three edge centers were calculated by the strain-smoothing method, which performed strain-smoothing operation directly on the three edges of a linear finite element instead of requiring an extra smoothing domain. In this way, not only could a linear strain field be constructed within an element, but strain consistency at the center of the element’s intersecting edges could also be ensured. The proposed ECSSE was adopted to manage membrane and bending strains. Meanwhile, the discrete shear gap (DSG) method was organically combined with the ECSSE for processing the shear strain to eliminate shear-locking. The ECSSE-DSG showed outstanding performance in a variety of tests, including those for plates, folded plates and curved shells; static, free vibration, dynamic, and buckling analyses; benchmark and engineering examples. High accuracy was obtained for both displacement and strain energy, there was no appearance of shear-locking, a smoother stress field was produced, and there was temporal stability. The excellent performance of the ECSSE-DSG when employed for engineering problems indicated its promising practical application prospects.

Static and free vibration analysis of sandwich shell panels using quadrilateral flat shell finite element

A quadrilateral flat-shell element with nine DOF (Degrees of Freedom) per node is developed for the static (deflections and stresses) and free vibration analysis (natural frequencies and accompanying mode shapes) of sandwich cylindrical and globular shell panels. The element is based on zigzag theory and is augmented using the discrete Kirchhoff quadrilateral bending plate element having seven DOF per node. It is vital to convert the rotations and translations degrees of freedom from local to global direction for the plate bending element to transform into a flat shell element. DKZigTS is developed by adding two fictitious degrees of freedom and has nine local and global DOF per node. The transformation matrix of size 36 × 36 is used for DKZigTS. It does not face the problem of the ill-conditioned stiffness matrix. The developed element is judged for its performance for simply supported and clamped shell panels. The DKZigTS element’s result are compared with results gotten using the 3 D finite element (FE) results of ANSYS (Mechanical APDL). To establish the confidence the comparison is also done with those 2 D analytical, 2 D numerical and 3 D elasticity results available in the literature. The numerical evaluation with DKZigTS element exhibits a very satisfactory performance for the static and free vibration response of moderately thick and thick sandwich spherical and cylindrical shell panels.