Grid Shell Structure Research Articles

Investigating the Influence of the Improved Multibody Rope Approach on the Structural Behavior of Dakar Mosque Gridshell Structure

Gridshell structures are characterized by an impressive strength-to-weight ratio, allowing their application in large-span roofing structures. However, their complex construction process and maintenance limited their widespread application. In recent years, the development of parametric and computational design tools has rekindled interest in this type of structure. Among these techniques, the Multibody Rope Approach (MRA) is a form-finding method based on the dynamic equilibrium of a system of masses (nodes) connected by ropes, which allows optimizing the structural shape starting from the dual geometry of the funicular network. To optimize the construction process, an improved version of the MRA, i-MRA, has been recently developed by the authors with the goal of uniforming the size of the structural components. To investigate the impact of the i-MRA method on the structural behavior of gridshell structures, the practical case of the design of a mosque roof is here analyzed. The comparison is carried out in terms of structural performance with respect to permanent and equivalent quasi-static loads. In addition, free-vibration natural-frequency shift is obtained by performing linear modal analysis. Finally, the global behavior with respect to buckling and elastic instability is assessed solving the relevant eigenvalue problem. The results demonstrate that for the roofing of the Dakar mosque, the structural configuration obtained through i-MRA is superior in terms of both construction efficiency and structural performance. The achieved shape exhibits a more uniform distribution of stresses induced by the applied loads together with very limited structural element typologies.

Seismic evaluation of isolation performance on single layer cylindrical reticulated shells supported along four sides

This study investigated the dynamic characteristics and seismic isolation performance of a single-layer cylindrical grid shell structure with lower support structures and different seismic isolation schemes, which encompass the installation of layered rubber bearings and new three-dimensional isolation bearings. Seven reduced-scale models of the structure were tested on a shaking table, with acceleration, strain, and displacement sensors positioned in typical locations. The results showed that the seismic response of the upper cylindrical grid shell structure was amplified by the lower support structure, which indicates that separate seismic designs for both the upper structure and lower support structure are unsafe. The use of layered rubber bearings at the foundation effectively reduced horizontal seismic response but amplified vertical seismic response. To address this issue, the new three-dimensional isolation bearing was proposed, which showed better overall seismic isolation performance compared to the rubber bearings. Additionally, a new seismic isolation scheme was proposed, using a combination of three-dimensional isolation bearings at both the foundation and column tops. This scheme showed superior seismic isolation efficiency compared to other schemes and can reduce the volume and installation difficulty of the three-dimensional isolation bearing. Considering the functional requirements, cost, and technical difficulty is crucial when selecting suitable seismic isolation measures since different schemes have their advantages and disadvantages and perform differently under various seismic conditions.

Stock Optimization of Naturally Curved Wood Logs on Freeform Truss Structures

This paper presents an optimization method for incorporating discarded naturally curved wood logs onto a freeform gridshell with a predefined topology. Though still little explored, the research field of reusing structural elements is experiencing increasing attention owing to its significant potential to reduce the environmental impact of building design. However, several constraints must be considered as the optimal structure depends on stock availability and the corresponding geometry and material properties of that given stock. Therefore, the focus is on determining the best configuration of stock elements considering the defined design objectives and constraints. The proposed method is a top-down approach, as the global topology of the structure is predetermined. Multi- objective optimization is conducted using the Strength Pareto Evolutionary Algorithm 2 (SPEA2) and a modified genetic algorithm with permutation encoding in the form of ordered crossover and scramble mutation. Furthermore, this paper introduces a Team-Based Repair (TBR) algorithm that increases the likelihood of each solution being valid for analysis. The performance of the optimization method is demonstrated on a curved gridshell structure, and the effect of the different design objectives and stock sizes on the final design is analyzed and discussed.

Novel Paradigm for Steel Joints in Gridshell Structures: from Structural Optimization to Advanced Construction

AbstractNovel integrated computer‐aided paradigm/workflow for the topology optimization (TO) and additive manufacturing (AM) of steel joints in gridshell structures is proposed. The architecture scheme of gridshell structure was first established and numerically analyzed through Grasshopper parametric platform. Based on the extracted joint geometric parameters and the corresponding loading conditions, the initial joint structures were parametrically modelled using the subdivision surface method. Further parametric TO design was accomplished by the bi‐directional evolutionary structural optimization (BESO) method on the basis of cloud computing server. A series of mesh smoothing and reverse modelling algorithms were applied to the optimized joint to obtain a closed smooth surface in the NURBS form, which was then output as STL file for additive manufacturing. One typical optimized joint was additively manufactured using selective laser melting. The proposed workflow can be extended to a much wider range of spatial structures with various joint types.

Additive manufacturing oriented parametric topology optimization design and numerical analysis of steel joints in gridshell structures

Additive manufacturing (AM) oriented joint topology optimization (TO) is a novel integrated computer-aided structural design and construction paradigm for spatial structures. This research proposed a complete computer-aided workflow for the TO design, numerical analysis and AM of steel joints in gridshell structures. A fully parametric TO design method for joints in gridshell structures was established based on the Grasshopper platform. The joints were automatically generated based on subdivision surface technology and then optimized using the bi-directional evolutionary structural optimization (BESO) algorithm. The structural performance of the optimized joints in terms of compliance, maximum displacement and maximum stress was studied through finite element analysis. The influences of various design parameters, including the loading condition, target volume and filter radius, on the structural performance of the optimized joints were investigated. The target volume was confirmed to have significant effect on the joint structural behaviour while the filter radius was found to affect the branch features of optimized joint. A practical design example of steel joints in single-layer cylindrical gridshell structure was presented to demonstrate the feasibility and validity of the proposed workflow. A typical optimized joint made of 316L stainless steel was additively manufactured using selective laser melting.

Structural performance of novel aluminium alloy gusset joints for connecting four I-section beam members

This paper presents the seismic behaviour of an aluminium alloy grid shell structure with due consideration of the rotation performance of its two novel gusset joints. The two novel aluminium alloy gusset joints were designed for connecting cross-arranged I-section beam members by stainless steel swage-locking pins and stainless steel bolts. One full-scale gusset joint was tested under monotonic loading, with the failure mode, load-displacement response and stiffness classification fully reported. The solid-based refined finite element (FE) model of the joint was developed by using Abaqus program and validated against test results. Based on the validated FE model, parametric studies were performed to investigate the effect of key parameters, including the shape of gusset plates, the preload of fasteners, angle shear connector configurations, and the number and layout of pins, on the structural performance of the novel gusset joints. The failure modes, moment-rotation curves, initial stiffness and ultimate design resistance were identified and compared in groups for joint design optimization. The cyclic behaviour of two optimal gusset joints was numerically analysed, and then incorporated in the fibre-based macro FE model of the aluminium alloy grid shell structure developed by using OpenSees program. The seismic performance of the grid shell structure subjected to different earthquake hazard levels, including the displacement, joint rotation, beam stress and shear base responses, was comprehensively evaluated. Sound earthquake resistance of the aluminium alloy grid shell structure is demonstrated, with safety and reliability of the novel gusset joints used in it.

Integrated design framework of 3D printed planar stainless tubular joint: Modelling, optimization, manufacturing, and experiment

Nowadays, tubular joints with superior structural properties have been extensively applied in constructing the complicated multi-planar steel joints that are often adopted in the grid shell structure system. However, sometimes it is challenging to maintain high-quality on-site welding joints or even difficult to assess the quality of on-site welding, especially for the overhead welding. This paper presents an integrated design framework of the 3D printed planar stainless tubular joint, and this framework is implemented by Solid Isotropic Material with Penalization Method (SIMP). Three joints with different brace to chord width ratios are optimized, and the re-engineered joints are obtained using computer-aided design software. Joints independently designed and manufactured by 3D printing methods can be riveted with other structural members to simplify the installation process and improve the construction efficiency, thus reducing the difficulty of on-site welding. Non-contact 2D DIC (Digital Image Correlation) is used to analyze the strain distribution more intuitively for 3D printed and welding planar tubular joints. Moreover, the coupon tensile test is proposed to analyze the stress–strain relationship when considering different printing orientations. Experiments show that the orientation of material additive manufacturing affects the yield strength, ultimate strength and elongation at fracture to a certain extent but has little influence on Young’s modulus. The optimized joint exhibits different failure modes than the traditional tubular joints, which can achieve strong-joint and weak-component mechanisms and avoid failure of the entire joint when local damage occurred. In addition, the plump curve according to the hysteresis loop suggests that the energy dissipation of the optimized joint is larger than the traditional welding joint, which is beneficial to enhance the seismic performance of the structures. The developed framework can also be extended to the complex spatial joints, which is subjected to multi-planar loads in the future.

Numerical Exploration on Snap Buckling of a Pre-Stressed Hemispherical Gridshell

AbstractMotivated by the observations of snap-through phenomena in pre-stressed strips and curved shells, we numerically investigate the snapping of a pre-buckled hemispherical gridshell under apex load indentation. Our experimentally validated numerical framework on elastic gridshell simulation combines two components: (i) discrete elastic rods method, for the geometrically nonlinear description of one-dimensional rods, and (ii) a naive penalty-based energy functional, to perform the non-deviation condition between two rods at joint. An initially planar grid of slender rods can be actuated into a three-dimensional hemispherical shape by loading its extremities through a prescribed path, known as buckling-induced assembly; next, this pre-buckled structure can suddenly change its bending direction at some threshold points when compressing its apex to the other side. We find that the hemispherical gridshell can undergo snap-through buckling through two different paths based on two different apex loading conditions. The structural rigidity increases as the number of rods in the gridshell structure becomes denser, which emphasizes the mechanically nonlocal property in hollow grids, in contrast to the local response of continuum shells. The findings may bridge the gap among rods, grids, knits, and shells, for a fundamental understanding of a group of thin elastic structures, and inspire the design of novel micro-electro-mechanical systems and functional metamaterials.

Structural analysis of GFRP elastic gridshell structures by particle swarm optimization and least square support vector machine algorithms

The gridshell structure is a kind of freeform structure, which is formed by the deformation of a flat grid and the final shape is a double curvature structure. The structural performance of the gridshell is usually obtained by finite element analysis (FEA), which is a time-consuming procedure. This paper aims to present a framework for structural analysis based on the machine learning (ML) model in order to reduce computational time. To this aim, design parameters including the length, width, height, and grid size of the structure are taken into consideration as inputs. The outputs are the member-stresses and the ratio of displacement to self-weight. Therefore, a combination of two algorithms, least square support vector machine (LSSVM) and particle swarm optimization (PSO), is considered. PSO-LSSVM hybrid model is applied to predict the results of the structural analysis rather than the FEA. The results show that the proposed hybrid approach is an efficient method for obtaining structural performance.

Dynamic scaling laws of spatial grid structures under inner explosion considering material and geometric distortions

It is a key issue to assure that the experimental results of scaled-down models of long-span spatial grid structure under inner blasting loads can truly reflect the characteristics of their prototype structure. The existing method to deal with the dynamic scaling laws of structures is not suitable for long-span spatial grid structures subjected to inner explosion. This paper derives and modifies the dynamic scaling laws among scaled-down models and full-size structure under inner explosion on the basis of dimensional analysis, taking long-span cylindrical grid shell structure as research case and considering the strain-rate effect, yield stress and dimension distortions. In this article, the improved scaling laws were verified and proved by comparing the simulation results with the test results of long-span cylindrical grid shell structure and its scaled-down models. The research results revealed that the maximum errors of the peak values of displacement responses and strain responses between the scaled-down model and the prototype were unacceptable without considering material and geometric distortions. Moreover, the empirical formulae to calculate the mass of explosive based on specific impulse were proposed and the corrected method to predict the inner explosion responses of full-size structure according to the results of scaled-down model tests was presented.

Hybrid Materiality

One of the most recognisable aspects of the digitalization of the design process is the increasing use of 3D printers and robots in the construction phases. When combining with analogue techniques, hybrid materiality in construction and architecture opens up significant application opportunities, but also challenges to the design process and production. In this study, the design and hybrid fabrication of a freeform gridshell structure, placed as a temporary installation in a public park, is presented. The structure was materialized in a hybrid combination of 129 wooden battens and 68 PLA 3D printed nodes, spanning 5 meters and reaching 2.5 m height. The examination of the challenges posed by the hybrid fabrication of the structure suggests that pre-conceived perceptions on production and installation stages should be reconsidered, and it highlights the importance of integrating material constraints and time limitations in the earliest phases of the design process.

Numerical Method for Direct Solution to Form-Finding Problem in Convex Gridshell

AbstractElastic gridshell is a class of net-like structure formed by an ensemble of elastically deforming rods coupled through joints, such that the structure can cover large areas with low self-weight and allow for a variety of aesthetic configurations. Gridshells, also known as X-shells or Cosserat Nets, are a planar grid of elastic rods in its undeformed configuration. The end points of the rods are constrained and positioned on a closed curve—the final boundary—to actuate the structure into a 3D shape. Here, we report a discrete differential geometry-based numerical framework to study the geometrically nonlinear deformation of gridshell structures, accounting for non-trivial bending-twisting coupling at the joints. The form-finding problem of obtaining the undeformed planar configuration given the target convex 3D topology is then investigated. For the forward (2D to 3D) physically based simulation, we decompose the gridshell structure into multiple one-dimensional elastic rods and simulate their deformation by the well-established discrete elastic rods (DER) algorithm. A simple penalty energy between rods and linkages is used to simulate the coupling between two rods at the joints. For the inverse problem associated with form-finding (3D to 2D), we introduce a contact-based algorithm between the elastic gridshell and a rigid 3D surface, where the rigid surface describes the target shape of the gridshell upon actuation. This technique removes the need of several forward simulations associated with conventional optimization algorithms and provides a direct solution to the inverse problem. Several examples—hemispherical cap, paraboloid, and hemi-ellipsoid—are used to show the effectiveness of the inverse design process.

BAMBOO CANOPY: TOWARDS A LIGHT CONSTRUCTION OF BAMBOO

ABSTRACT Despite the abundance of highly sustainable bamboo, people tend to overlook its structural performance for construction purposes. This paper therefore explores the potential of bamboo architecture to develop light-weight building systems and also to create an effect of lightness. Developed by a team at the School of Architecture of Southeast University, Bamboo Canopy is an outdoor stage canopy in Anji, China, that pushes the boundaries of bamboo as a material for building woven gridshell structure. The work is designed as a long-lifespan bamboo structure, with the design team and locals participating in its construction. Positioned on a public stage, Bamboo Canopy experiments with the combination of sustainable construction and local craftsmanship to produce a highly engaging architectural intervention that activates the existing place. With its wing-like form, it invites visitors to join the performance scene—as they approach the shell, the structure reveals itself—with a 12.4-metre span and 6-metre roof overhang, the canopy covers more than 150 square metres with only 1.2 square metres touching the ground. Through analysing the form, structure and details of this experimental project, this paper clarifies not only the potentiality but also the feasibilities in using bamboo for light construction.

From file to factory: Innovative design solutions for multi-storey timber buildings applied to project Zembla in Kalmar, Sweden

A “file-to-factory” process of computer technology is a way to both maximise efficiency throughout the building process, increase a building׳s performance, and be able to add interesting architectural possibilities throughout the design phase. The authors investigate a novel approach that produces a set of building trajectories rather than a set of buildings, yet yields a series of build-able examples of those trajectories. This paper evaluates how this series of stacked multi-storey timber buildings can be both incorporated within a file-to-factory process, and give rise to creating new innovative solutions throughout the entire design and manufacturing process.This process is applied to a real Swedish project called Zembla. It redefines the notion of sprawl, turning it into a progressive tactics for linking the city fabric to rural areas. It is a post-sustainable file-to-factory-produced timber ground-scraper; soaring above ground and water, suggesting a new way of making city-sized buildings for the future.A plug-in grid-shell structure is designed to contain a minimal amount of timber elements, beams make up the lattice, cross-laminated panels add structural support, surfaces come together to form the living capsules. Having the structure undulate across the topography and touching the ground in as few places as possible uses the dichotomy between landscape and urbanism, bringing the city to the people living in less densified areas. Each living unit is customised to its topological conditions within the grid.

Discrete elastica for shape design of gridshells

This paper presents an approach to designing a gridshell structure, which is constructed connecting beams under bending deformation by hinge joints. The gridshell is modeled as an assembly of piecewise linear curves called ‘discrete elastica’, which is a discretized form of elastica defined as the shape of buckled beam-column with large deflections. Shape parameters such as span, height at the support, height at the internal joint, and the external moments are assigned to generate various shapes of discrete elastica, which are found by minimizing the total potential energy. It is shown in the numerical examples that a gridshell surface designed using discrete elastica has small interaction forces between the curved beams at joints. Large deformation analysis is carried out for verification of the shape generated using discrete elastica. An optimization approach is presented to further reduce the interaction forces between beams by assigning specified number of ‘hinge + slot joints’ to allow relative translational displacement at a hinge. Finally, the static structural characteristics of optimal gridshells are investigated.

Bending Bamboo Rules: Beyond Century-Old Typologies

The ZCB Bamboo Pavilion, built in Hong Kong in 2015, is the largest bending-active bamboo gridshell structure to date. Globally, Hong Kong is one of the last places where raw bamboo is actively used in everyday construction. Yet, despite being ecologically sustainable, bamboo craftsmanship is slowly dissipating. Through several observations, discoveries, and projects, this paper discusses the sequential journey that generated a bold alternative to pre-existing local bamboo building typologies, challenging general perceptions and building regulations. The trade itself is not giving another path, but is receiving it as an alternative to fading away. Hence: by infusing digital technology into the design and construction process of a century-old building method, a fading vernacular tradition offers an alternative course of action centered on computational design.

Role of global buckling in the optimization process of grid shells: Design strategies

The aim of the paper is to propose a new approach for the optimization of grid shell structures based on a mixed sizing/topologic process, which specifically accounts for the global buckling behavior. The approach consists of merging a sequence of sizing and topological optimization processes where local and global buckling phenomena are opportunely introduced. Indeed, in addition to the removal of some members and the increase/decrease of the cross section size of the remaining ones, the proposed approach accounts for the possibility to convert some of the elements composing the grid shell structure, generally trusses, into beam elements with the aim of having an optimized solution also with respect to the global buckling behavior. The selection of the truss members to convert into beams is made by considering two different strategies presented in detail in the paper. Numerical analyses referring to some case studies derived from the current literature are developed by considering the proposed approach and a traditional sizing/topologic mono objective approach. The results obtained from the numerical analyses clearly underline the reliability of the proposed approach and its efficiency in comparison to traditional approaches of structural optimization.

Production phases and market for timber gridshell structures: A state-of-the-art review

Timber gridshell is a structure with a doubly curved shape that is made of grid timber laths. Gridshell structure can be a solution of interest in modern free-form structures that are environmentally sustainable. However, there is a lack of academic research focusing on the potential markets and the production stages based on this construction technology. The aim of this literature review is to investigate the gridshell structure to identify its global production process, as well as the partners involved in the architectural examples studied. A review of both peer-reviewed scientific articles and grey literature resources (e.g., magazines, web pages, etc.) was conducted to gather information about timber gridshells. The design examples found were categorized as small, medium, and large gridshells. The categorization is based on the size and level of complexity of the design examples. Production phases and partners involved in the design and construction of these structures were identified for each category. Furthermore, the motivations and barriers to using gridshell designs in construction, and the potential market segments were determined.

Production Phases and Market for Timber Gridshell Structures: A State-of-the-Art Review

Timber gridshell is a structure with a doubly curved shape that is made of grid timber laths. Gridshell structure can be a solution of interest in modern free-form structures that are environmentally sustainable. However, there is a lack of academic research focusing on the potential markets and the production stages based on this construction technology. The aim of this literature review is to investigate the gridshell structure to identify its global production process, as well as the partners involved in the architectural examples studied. A review of both peer-reviewed scientific articles and grey literature resources (e.g., magazines, web pages, etc.) was conducted to gather information about timber gridshells. The design examples found were categorized as small, medium, and large gridshells. The categorization is based on the size and level of complexity of the design examples. Production phases and partners involved in the design and construction of these structures were identified for each category. Furthermore, the motivations and barriers to using gridshell designs in construction, and the potential market segments were determined.

Lightweight Grid Shell Pavilion - Design, Manufacture and Erection of Full Scale Grid Shell Prototypes

AbstractThe main goal of author’s research is to design and construct grid shell structures, which are subsequently realized as experimental structures in full scale. These structures should make the place suitable for various events and also a friendly, pleasant, relaxing and free time space. By thinking about how such structure should look like and what materials and structure types are suitable, there were many kinds of lightweight structures considered.The most logical solution is to create a grid shell structure combining with a single layer membrane that would fulfill all aspects of elegant remarkable lightweight structure using some original details and workflow advancements. These grid shell projects should demonstrate another possibility to build and think about unconventional structures and provoke a deeper interest in these unique structures. The goal of this project was to create a feasible design of a grid shell structure and to build up the structures while being capable to understand the core of such an interesting phenomenon.