Hypar Shells Research Articles

Parametric design and modular construction of a large additive-manufactured hypar shell structure

Despite recent advances in additive manufacturing technologies, challenges remain to build 3D-printed structures at the architectural scale due to the high cost of large printing equipment. To address this challenge, modular construction has demonstrated its merit by making smaller prefabricated components and using on-site assembly. This paper presents a case study of a 3D-printed hypar shell structural art using modular construction. Guided by parametric design and structural analysis, we optimized the hypar shell to form a butterfly-like shape with a hollow-out pattern. The prefabrication of modular units was completed using commercial 3D printers to catch a limited production time. The prefabricated modular unit of the hypar shell was assembled on site for the Guangzhou International Light Festival, in which the lighting effect was added through the adjustable transparency of hollow spaces within the sandwiched panels. The 3D-printed hypar shell was also disassembled and rebuilt in the UK, showcasing the adaptability and flexibility of the modular design. The resulting 3D-printed structural art not only provides unique aesthetics for the built environment but also demonstrates the possibility of building large shell structures with a low budget by reducing complex falsework.

A study of impact induced stress due low velocity impact on laminated composite skewed hypar shell roof

The doubly ruled hypar shell, being one of the most feasible shell roof configurations, enjoys industrial preference for covering large column free areas. This class of shells is unique as the only curvature here is the cross curvature and these do not admit easy closed form solution particularly when the boundary conditions are complicated. Laminated composite, an innate choice to different industrial sectors for its huge specific strength and stiffness, good weathering resistance, is now being extensively employed in civil engineering. However the low transverse shear strength of the composite shell impelled the researchers to study the response of the same under the action of impact loads. In the present study, a finite element code is functioned to investigate the impact induced stress history generated in simply supported laminated composite hypar shell for different impact velocities of a spherical solid striker. Contact behavior is described by modified Hertzian contact law where as time dependent equations are solved using Newmark’s time integration algorithm in present analysis. A practicing engineer often has to select a particular shell option consisting stacking sequence among a number of possibilities. The present paper discusses the behaviour of composite hypars under low velocity impact and different stresses induced due to the same from engineering standpoint to propose a selection guide line among the available options and to proposes values of practical parameters like the equivalent static loads and dynamic magnification factors for designing such shells through static simplification of the problems.

On Nonlinear First Ply Failure Study of Laminated Composite Thin Skewed Hypar Shell Roofs

The skewed hypar shells have gained immense popularity in practical civil engineering fields due their highly aesthetic look. Light weight laminated composite material has increased its wide acceptance day by day in practical structures by virtue of superior material properties like high strength, high stiffness to weight ratio, prolonged fatigue life etc. Different types of bending as well as free and force vibration studies of laminated composite skewed hypar shells were done by earlier researchers. In some literatures, the first ply failure was also investigated using geometric linear strains only. So, the present paper aims to study the first ply failure behaviour of laminated composite skewed hypar shell roofs considering geometric nonlinearity. An eight noded isoparametric curved finite element having five degrees of freedom at each node is used here for finite element method. To establish the correctness of the present approach different benchmark problems are solved in this paper. Various types of lamina stacking sequences are taken up by the authors’ problems for first ply failure analysis of symmetric and antisymmetric skewed hypar thin shells with practical boundary condition. Along with the maximum stress and maximum strain failure criteria the authors use interactive failure criteria like Hoffman, Tsai-Hill and Tsai-Wu criteria as well as failure mode based criteria like Hashin and Puck criteria for the present study. The results obtained from this numerical investigation are analysed and post processed from different engineering standpoints to extract meaningful conclusions regarding first ply failure behaviour of the composite skewed hypar thin shells and to arrive at important practical guidelines which are expected to be beneficial for practicing civil engineers.

Design of experiments analysis of fundamental frequency of laminated composite hypar shells with cut-out

The effect of lamination angle (A), width-to-thickness ratio (B), cut-out location along x-direction (C) and cut-out location along y direction (D) on fundamental frequency of hypar shells made of laminated composites is considered using Taguchi robust design concept. Finite element analysis is done to obtain fundamental frequency of the structure for different parametric variation. Three levels of each parameter are considered to form L27 orthogonal array in order to maximize fundamental frequency. Main effect plot identifies the significant parameters. Optimal condition for maximum fundamental frequency is obtained as 45° lamination angle, width-to-thickness ratio of 20, cut-out location along x-direction 0.4 and along y-direction 0.3 (A2B1C3D2). Interaction plots locate the interaction effects between selected parameters. Analysis of Variance study evaluates the significant parameters and their contribution on output, i.e., fundamental frequency. Current investigation reveals, width-to-thickness ratio of shell is the most significant factor while lamination angle and cut-out location have little significance. Among the interacting parameters, interaction between lamination angle & cut-out location (A × C) and interaction between width-to-thickness ratio & cut-out location (B × C) have some significance. Width-to-thickness ratio (B) has 96.76% contribution while lamination angle (A) and cutout locations (C & D) and interactions have low contribution. Residual plots for fundamental frequency are considered and confirmation test validates the present analysis. S/N ratio is found to improve by 12.43% compared to the initial condition.

Influence of the concrete strength and the type of supports on the stress-strain state of a hyperbolic paraboloid shell footbridge structure

Relevance. This work is the first in a series of publications on the selection of a suitable analytical surface for implementation as a self-supporting structure for a thin shell footbridge. The study on the influence of concrete strength, live load position and support types on the stress-strain state of a hyperbolic paraboloid (hypar) shell is presented. Objective - to define the initial design parameters such as the appropriate concrete strength and the support type that generates the best structural behaviour to perform the subsequent structural design of a thin shell footbridge. Methods. The static finite element analysis was performed for 4 compressive strengths of concrete (28, 40, 80, 120 MPa) which correspond normal, high and ultra-high resistance concrete, 5 different live load arrangements and 3 different support conditions. Results. The shell model with pinned (two-hinged) supports shows the same vertical displacements as the model with fixed supports (hingeless). For the studied shell thickness, in terms of stress behaviour, the model with pinned ends is more efficient. The combination of two-hinged supports with 80 MPa concrete strength shows a better structural performance.

Finite element prediction of first-ply failure loads of composite thin skewed hypar shells using nonlinear strains

The application of skewed hypar shell as civil engineering roofing unit is an established fact. Such use has gained a greater momentum when this shell is fabricated with advanced materials like the laminated composites. Research attempts in studying the first ply failure behaviour of laminated composite structural units are common now among engineers and the novelty of this paper lies in continuation of such efforts being applied to composite skew hypar shell. For accurate modelling of the failure behaviour of this thin shell, nonlinear strains are considered together with eight noded isoparametric serendipity finite element. Different well-established failure criteria including the failure criterion of Puck are used to extract the first ply failure pressure values, failure locations and failure modes as well. The finite element code developed is used for numerical experimentation with parametric variations and the results are post processed and interpreted to extract meaningful engineering conclusions.

A new efficient two-stage method for damage localization and quantification in shell structures

The article proposes a new efficient two-stage approach for damage localization and quantification in shell structures using a modal flexibility sensitivity-based damage indicator abbreviated as MFBDI and a recently developed parameter-free optimization algorithm named golden ratio optimization method (GROM). In the first stage, the damage indicator MFBDI is employed to localize possible damage elements in the monitored shell structure. These possible damage elements also help define the search space of optimization problem in the next step. In the second stage, the GROM as a robust optimization solver is implemented to update the finite element (FE) model of the shell structure for refined localization of damage and quantification of its severity. The accuracy and efficiency of the proposed two-stage approach are demonstrated by two numerical simulation examples including a hypar shell and a spherical shell. The simultaneous influences of spatially-incomplete and inaccurate vibration data on damage prediction results are also taken into consideration. The obtained results reveal that the proposed approach can provide an efficient and accurate damage localization and quantification procedure for the studied shell structures.

Fem Analysis of Progressive Failure for Composite Hypar Shells

The finite element method is used to to study progressive failure aspects of laminar composite skewed hypar shells with straight edges employing the eight-node isoparametric element in linear and elastic ranges under uniformly distributed static loading. A stiffness decrease scheme is proposed in which the stiffness properties of the failed element are gradually reduced resulting in redistribution of eveloping stresses on the extent of damage it accumulates. Specific numerical problems of earlier investigators are solved to validate the present approach. Numerical experiments are further carried out for different parametric variations, including some complicated boundary conditions and stacking orders of practical importance to obtain the first ply and progressive failure loads. Well accepted failure criteria are used to evaluate the failure loads and its development. Progressive failure in hypar shells are examined to arrive at some conclusions useful to the practicing engineers regarding tailoring guidelines of laminar composites and planning of nondestructive test programs for their health monitoring.

Bi-axial and shear buckling of laminated composite rhombic hypar shells

The bi-axial and shear buckling behavior of laminated hypar shells having rhombic planforms are studied for various boundary conditions using the present mathematical model. In the present mathematical model, the variation of transverse shear stresses is represented by a second-order function across the thickness and the cross curvature effect in hypar shells is also included via strain relations. The transverse shear stresses free condition at the shell top and bottom surfaces are also satisfied. In this mathematical model having a realistic second-order distribution of transverse shear strains across the thickness of the shell requires unknown parameters only at the reference plane. For generality in the present analysis, nine nodes curved isoparametric element is used. So far, there exists no solution for the bi-axial and shear buckling problem of laminated composite rhombic (skew) hypar shells. As no result is available for the present problem, the present model is compared with suitable published results (experimental, FEM, analytical and 3D elasticity) and then it is extended to analyze bi-axial and shear buckling of laminated composite rhombic hypar shells. A C0 finite element (FE) coding in FORTRAN is developed to generate many new results for different boundary conditions, skew angles, lamination schemes, etc. It is seen that the dimensionless buckling load of rhombic hypar increases with an increase in c/a ratio (curvature). Between symmetric and anti-symmetric laminations, the symmetric laminates have a relatively higher value of dimensionless buckling load. The dimensionless buckling load of the hypar shell increases with an increase in skew angle.

Betonarmede Strüktürel Bir Zirve: Hipar Kabuklar

Betonarmede Strüktürel Bir Zirve: Hipar Kabuklar

Mode frequency analysis of antisymmetric angle-ply laminated composite stiffened hypar shell with cutout

Abstract This article deals with finite element method for the analysis of antisymmetric angle-ply laminated composite hypar shells (hyperbolic paraboloid bounded by straight edges) that applies an eight-noded isoparametric shell element and a three-noded beam element to study the mode-frequency analysis of stiffened shell with cutout. Two-, 4-, and 10-layered antisymmetric angle-ply laminations with different lamination angles are considered. Among these, 10-layer antisymmetric angle-ply shells are considered for elaborate study. The shells have different boundary conditions along its four edges. The formulation is based on the first-order shear deformation theory. The reduced method of eigen value solution is chosen for the undamped free vibration analysis. The first five modes of natural frequency are presented. The numerical studies are conducted to determine the effects of width-to-thickness ratio (b/h), degree of orthotropy (E 11/E 22), and fiber orientation angle (θ) on the nondimensional natural frequency. The results reveal that free vibration behavior mainly depends on the number of boundary constraints rather than other parametric variations such as change in fiber orientation angle and increase in degree of orthotropy and width-to-thickness ratio.

Application of FEM on first ply failure of composite hypar shells with various edge conditions

This study aims to accurately predict the first ply failure loads of laminated composite hypar shell roofs with different boundary conditions. The geometrically nonlinear finite element method (FEM) is used to analyse different symmetric and anti-symmetric, cross and angle ply shells. The first ply failure loads are obtained through different well-established failure criteria including Puck\'s criterion along with the serviceability criterion of deflection. The close agreement of the published and present results for different validation problems proves the correctness of the finite element model used in the present study. The effects of edge conditions on first ply failure behavior are discussed critically from practical engineering point of view. Factor of safety values and failure zones are also reported to suggest design and non-destructive monitoring guidelines to practicing engineers. Apart from these, the present study indicates the rank wise relative performances of different shell options. The study establishes that the angle ply laminates in general perform better than the cross ply ones. Among the stacking sequences considered here, three layered symmetric angle ply laminates offer the highest first ply failure load. The probable failure zones on the different shell surfaces, identified in this paper, are the areas where non-destructive health monitoring may be restricted to. The contributions made through this paper are expected to serve as important design aids to engineers engaged in composite hypar shell design and construction.

First ply failure analysis of laminated composite thin hypar shells using nonlinear finite element approach

In this paper the nonlinear finite element approach is used to solve the problems of first ply failure of laminated composite skewed hypar thin shell roofs. The geometrically nonlinear strains terms are incorporated in the present finite element code which is validated through solution of the problems solved and published by earlier researchers. The first ply failure loads of the industrially popular, aesthetically appealing hypar shells are studied meticulously for varying aspect ratios and thicknesses for clamped boundary condition. The paper gives specific recommendations regarding choice of linear and nonlinear approaches for obtaining failure loads in different specific cases.

Simply supported composite hypar shells under free vibration–some observations

A general finite element procedure is presented to model the hypar shells using eight ndash noded curved quadratic isoparametric elements with five degrees of freedom per node including two inplane displacements and one transverse displacement and two rotations Problems of twisted cantilever plate which have structural resemblance with skewed hypar shell are solved using the present approach and the results are compared with published ones Having established the exactitude of the present formulation numerical experiments with simply supported skewed composite hypar shells are conducted for four different types of laminations including four layered symmetric and antisymmetric cross and angle ply laminates The first four natural frequencies are presented in tabular forms and are studied critically and a set of meaningful conclusions are derived nbsp

Free vibration analysis of antisymmetric angle ply laminated composite stiffened hypar shell with cut out

Laminated composite shells are frequently used in various fields of engineering like aerospace, mechanical, marine and automotive engineering. Among different types, hyperbolic paraboloid shell bounded by straight edges (hypar) is aesthetically appealing, provides ease of casting and used as roofing units in large column free areas. Cutout is generally provided in roof structures to allow entry of light, for ventilation purpose, to enhance accessibility of other parts of the structures and sometimes to alter the resonant frequency. An attempt has been made using finite element method for the analysis of stiffened hypar shell with cut out that applies an eight noded is oparametric shell element with five degrees of freedom and a three noded beam element for stiffeners. The study deals with vibration analysis of a hypar shell stiffened along the margin of cut outs with different boundary conditions and antisymmetric angle ply lamination. The formulation is based on first order shear deformation theory. The reduced method of eigen value solution is chosen for the undamped free vibration analysis. The numerical studies are conducted to determine the effects of degree of orthotropy (${E_1}/{E_2})$.,ibre orientation (θ) and width to thickness ratio (b/h) on the non-dimensional fundamental frequency. The results are given in graphical form and obtained results are compared.

Changing Butterfly: a Large 3D Printing Work Based on Structural Mechanics

How to realize mechanical butterfly-like shell and design efficient construction details for resembling, posed problems and challenges to the design and construction of a large 3D printing work. Firstly, through analysis of the synergetic mechanism of butterfly-like morphology and structural mechanic of Hypar shell, digital design methods and adjusting modes were well studied. Secondly, based on the features of additive manufacturing, adaptive methods of unit division and construction were proposed and discussed. Moreover, changing modes of lights were tested through the combination of photoelectric numerical control and corresponding details design. As a result, not only the construction of 3D printing work of large scale butterfly-like shell, but also more than 100 new changing patterns of lights were realized.

Finite Element Analysis of HYPAR Shell Footings with Variation in Edge Beam Dimensions and Embedment Ratio

This investigational study involves analysis of settlement characteristics of HYPAR shell footings with variation in the edge beam sizes using a finite element code-PLAXIS. HYPAR shell footings have been known to bring about economy in regions with high material to cost ratio when compared to flat slab footings. This study strengthens the case of HYPAR footings by confirming its superiority in the aspect of lower settlement characteristics. The effects of changing the embedment ratio on the aspect of settlement, load bearing and soil-shell interphase stresses have also been studied.

Modal Analysis of Hipped Hypar Shell by Using ANSYS

Modal Analysis of Hipped Hypar Shell by Using ANSYS

Deflection, forces and moments of composite stiffened hypar shells with cutout

Among the various forms of doubly curved shells, hypar shell is aesthetically appealing and used as roofing units in large column free areas. Cutout is in general provided in roof structures to allow entry of light, venting and to enhance accessibility of parts of the structure, and sometimes to alter the resonant frequency. Though some studies are available for other forms of shells, very few literatures appear to have been published on the effects of cutouts on bending behavior of hypar shell. Finite element method using an eight noded shell element and a three noded beam element both curved and isoparametric is applied to analyze the bending behavior of stiffened hypar shell with cutout. Hypar shell stiffened along the margin of cutouts under the same intensity of loading and different boundary conditions for antisymmetric angle ply lamination is studied for five types of cutouts. The displacements, force and moment resultants are computed at the nodal points of different boundary elements around the openings. The comparative performance of shell characteristics around the opening for different cutouts including longitudinal and transverse of equivalent size reveals that size of the opening is a governing criterion to determine the shell characteristics. Also boundary constraints have large impact on deflection and static stress resultants.

Bending analysis of laminated stiffened hypar shell roofs with cutout

A review of existing literature reveals that bending analysis of laminated composite stiffened hypar shells with cutout is scanty.Skewed hypar shell is aesthetically appealing and being doubly ruled provides ease in casting. Further, this type of shell allows entry of north light making it suitable as civil engineering roofing units. Hence an extensive study of antisymmetric angle-ply laminated composite stiffened hypar shells with cutout for different type of practical boundary conditions isconsidered under same intensity of loading. However, results having maximum practical implications are analyzed herefor the sake of brevity.The shell combinations among a number of possible options arechosen. The shell characteristics along some typical lines of dominating values of the respective shell characteristics are studied for different lamination angles.