Research on Digital Construction Technology for Special-Shaped Shell Pipe Structures

Abstract

The aesthetic appeal of special-shaped shell pipe structures makes them highly favored by architects and holds promising prospects for various applications. In the detailed design stage, NURBS curves should be divided into multiple continuous arcs due to the limitations of current steel structure fabrication equipment, which can only accommodate pipes with equal-curvature bends. However, the traditional manual fitting methods suffer from several issues including low efficiency, undercutting at the interface, poor smoothness of curves, and lack of control over tolerances. Furthermore, the weaker out-of-plane stiffness and utilization of bending arc pipe sections pose significant challenges in terms of spatial positioning and installation accuracy that need to be addressed. The study focuses on addressing these challenges by investigating digital construction technology for special-shaped shell pipe structures and developing a parametric algorithm that enables automatic fitting of spatial NURBS curves into multiple arcs, thereby achieving seamless curve fitting. A post-processing program was developed to enable the parametric generation of fabrication and installation information for structural members, which can be seamlessly integrated into the BIM database. Finally, structural position control technology is proposed to improve assembly efficiency and ensure consistency between the completed construction state and the design shape. The above digital construction technology has been applied in projects such as the Haihua Island International Conference Center. It can provide complete technical solutions for modeling of special-shaped shell pipe structures, including establishment of a member information database, fabrication at the workshop and installation on site, construction organization management, as well as installation accuracy control.

1. Introduction

A special-shaped shell pipe structure (Figure 1) is a kind of complex structure that realizes special-shaped surface modeling by bending arc pipe. Its member axis is mostly a non-uniform rational B-splines (NURBS) curve [1], which can be used to accurately present standard or free-form geometric shapes, and varies in the curvature, furthermore it is usually a two-way bending arc member.

The excellent performance of special-shaped shell pipe structures in architecture [2,3] leads to its wide application, but also introduces many difficulties and challenges during construction.

Currently, research on these structures primarily focuses on static and dynamic performance analysis [4], morphogenesis of the special-shaped surface structure [5,6], and shape and topology optimization of the surface [7]. However, there has been limited research conducted on the detailed design [8], manufacturing processing [9], installation accuracy [10], and digital construction [11] of special-shaped shell pipe structures. For numerous intricate and diverse nodes in the Morpheus Hotel project, Piermarini [12] incorporates a combination of four software programs, namely Grasshopper, Midas, RSA, and Excel, to effectively execute digital construction tasks such as node classification, detailed modeling, batch drawing, and three-dimensional digital model expression. This serves as an exemplary application of computational engineering. For the design and construction of the Phoenix Center, Zhou [13] developed Digital Project, a 3D modeling software based on the CATIA platform, to construct a more precise and comprehensive multi-disciplinary digital model. Numerous pieces of intricate building information in 3D format were processed by extracting crucial data from the DP (CATIA) model created by architects, importing this information into a Rhino model, and subsequently exporting the Rhino model into CAD for generating workshop drawings.

When constructing such structures, two main challenges arise:

For special-shaped shell structures with a box section, the bending arc box members can easily achieve the variation effect of NURBS curve curvature by adapting a non-mold formation machine. However, for special-shaped shell pipe structures, current steel structure fabrication equipment can only perform equal-curvature bending on pipes [9,14]. Due to the fabrication limitation, NURBS curves need to be divided into several continuous arcs during the detailed design stage. The process is anticipated to inevitably yield certain fitting errors, and architectural designers generally impose stringent requirements on such errors. However, as the error control becomes stricter, there is an increase in the number of curved segments obtained after fitting, leading to a comprehensive reduction in the length of each segment [15]. The precision control of the bending circle processing becomes more challenging as the section length of the bending circle decreases, leading to heightened difficulty in controlling the ellipticity, wall thickness thinning amount, and bending circle rebound amount for steel pipe. Consequently, there is a potential increase in rework rate for the member.

The conventional manual fitting method for NURBS curves in constructional engineering is inefficient due to its inability to accurately and promptly quantify curve fitting deviations [8,9]. Inadequate continuity at segment points leads to gaps and overlaps at the weld interface between adjacent curved members. Secondary cutting of the interface during fabrication negatively impacts the building’s aesthetic appearance. Innovative methodologies for NURBS curve fitting, such as the accumulated chord length parameterization method [16], and intelligent algorithms such as the genetic algorithm [17] and the deep learning algorithm [18], aim to minimize segment count while ensuring accuracy, reducing processing complexity. Thus, there is an urgent need for improved fitting methods in constructional engineering.

Current practice mainly relies on shop drawing [8] to convey member information for spatial steel structures, which cannot efficiently interact and update the member information. It is difficult to establish a real-time visualized BIM model to guide the construction procedure [19,20,21]. Moreover, an unreasonable construction method will cause large structural deformation due to the irregular shape and weaker out-of-plane stiffness of special-shaped shell pipe structures [4,10,22]. Thus, stricter requirements are imposed on positional control of special-shaped shell pipe structures.

In order to address considering the challenges associated with constructing special-shaped shell pipe structures, a parametric approach for automatically fitting a space NURBS curve into a multi-segment arc curve, thereby achieving automatic curve fitting is proposed firstly in Section 2. Additionally, an all-encompassing digital project management is achieved by implementing the post-processing procedure for structural member information in Section 3. This enables the generation of bending member processing information and installation details in the BIM database program. To address the challenge of configuration control for special-shaped shell pipe structures, Section 4 introduces a three-dimensional structural pre-camber method during the detailed stage to ensure precise manufacturing and assembly of members. Finally, Section 5 presents a comprehensive digital construction technology and application for special-shaped shell pipe structures, offering complete technical solutions encompassing detailed modeling, establishment of a member information database, fabrication at the workshop and installation on-site, construction organization management, as well as installation precision control.

2. NURBS Curve Parametric Fitting Technology

For special-shaped shell pipe structures, the primary problem in the construction is how to convert NURBS curves into equal-curvature arcs that can be used for fabrication ensuring architectural appearance [23].

2.1. Degree and Continuity of Curve

The degree of curve represents the smoothness of curve and is a positive integer. Lines and polylines are usually degree 1, circles are degree 2, and most free-form NURBS curves are degree 3 or 5.

For a degree-k NURBS curve, it can be expressed by a piecewise rational polynomial:

$$f(u)={\displaystyle \frac{{\displaystyle \sum _{i=0}^n{\omega }_i{P}_i{N}_{i,k}(u)}}{{\displaystyle \sum _{i=0}^n{\omega }_i{N}_{i,k}(u)}}}$$

(1)

where ${\omega }_i$ is the weight of control points; $P_i$ is control points; $N_{i,k}(u)$ is degree-k spline basis function; and $u$ is node vectors.

In a mathematical view, for a degree-k NURBS curve in a plane, combing with Taylor expansion, the degree-k spline function at $x=a$ is:

$$P_k(x)=f(a)+f^{\prime }(a)·(x-a)+{\displaystyle \frac{f^{″}(a)}{2!}}·{(x-a)}^2+{\displaystyle \frac{f^{‴}(a)}{3!}}·{(x-a)}^3+\cdots {\displaystyle \frac{f^{(k)}(a)}{k!}}·{(x-a)}^k.$$

(2)

For given fitting error $e$, the degree-k spline function at $x=a$ can be reduced into degree-k-1 with the condition ${\displaystyle \frac{f^{(k)}(a)}{k!}}·{(x-a)}^k\le e$. The fitting degree-k-1 spline function can be expressed as:

$$P_{k-1}(x)=f(a)+f^{\prime }(a)·(x-a)+{\displaystyle \frac{f^{″}(a)}{2!}}·{(x-a)}^2+{\displaystyle \frac{f^{‴}(a)}{3!}}·{(x-a)}^3+\cdots {\displaystyle \frac{f^{(k-1)}(a)}{(k-1)!}}·{(x-a)}^{k-1}$$

(3)

Thus, for a degree-k NURBS curve, within an allowable error range, the curves near multiple control points can be reduced into a degree-k-1 NURBS curve. However, reducing the degree of the curve will decrease its smoothness and obviously change its shape. At present, the equal-curvature bending arc pipe whose axis is a degree-2 curve can only be fabricated, and degree-3 or degree-5 curves cannot be directly manufactured. It is necessary to reduce the curve degree to meet the fabrication requirements.

In addition, the smoothness of the transition between contiguous curves can be expressed by curve continuity (Figure 2). Continuity has different levels, from low to high: G0 (position continuous), G1 (tangent continuous), G2 (curvature continuous), and G3 (curvature rate continuous).

G0 (position continuous) (Figure 2b): It only has overlapping ends, and the tangent direction and curvature at the joint are inconsistent. The resulting curve will have a sharp seam, representing the lowest level of continuity. Pipes based on G0 continuous curves may exhibit undercut phenomena at the interface (Figure 3), thus requiring processing to achieve at least G1 continuity.

G1 (tangent continuous) (Figure 2c): Not only do the endpoints overlap at the junction, but they also have the same tangent direction. This G1 continuous curve avoids sharp joint seams; however, there is still a discernible difference in visual effect due to the abrupt change in curvature at the junction, resulting in a perceived curve discontinuity.

G2 (curvature continuous) (Figure 2d): It not only satisfies the characteristics of the aforementioned two levels of continuity, but also ensures identical curvature at the joint (which can be 0). The G2 continuous curve exhibits a seamless and smooth visual effect without any abrupt transitions or sudden changes in curvature. This level of continuity is typically considered as the minimum requirement for achieving smooth curves.

G3 (curvature rate continuous) (Figure 2e): This continuous level of curves has a smoother visual effect than G2. However, it is usually used only in automotive design because of the need for higher-order curves or more curve fragments. This continuous level not only has the characteristics of the continuous level above, but also the rate of change in curvature at the junction is continuous, which makes the change in curvature smoother.

2.2. NURBS Curve Fitting Multi-Segment Arc Method

NURBS curves in an architectural model are generally degree-3 curves. The original degree-3 curve is initially reduced to degree-2 during the fitting process. Subsequently, the points of curvature discontinuity on the new degree-2 curve are identified and utilized as segment points for the curve. Ultimately, the original degree-3 curve can be converted into many segments of arcs with G1 tangent continuous at the segment point. The difference between the architectural model and fitting model is relatively too small to distinguish with the naked eyes, but it greatly reduces the difficulty of steel structure fabrication. In case of reduced degree fitting and continuity control of NURBS curves, a multi-segment arc fitting method is proposed, which can automatically convert the spatial NURBS curve into a multi-segment arc curve and automatically adapt G1 tangent continuous between two adjacent arc curves. The specific fitting methods are as follows:

• Through the curvature analysis of a given degree-3 NURBS curve, it is showed that the curve continuity is continuous G2 curvature and there are G3 discontinuous points (Figure 4a).
• Within a given deviation range, the genetic algorithm is used to perform degree-reduction fitting on the original NURBS curve and construct a new degree-2 NURBS curve.
• The curvature analysis shows that the new degree-2 NURBS curve is G1 tangent continuous and there are G2 discontinuous points. Find the G2 curvature discontinuous points of the curve (Figure 4b).
• By utilizing the G2 discontinuous points of the new degree-2 NURBS curve as breakpoints, a single circular arc is used to connect each segment point with the tangent line at the starting point of the curve. Thus, based on two endpoints and one tangent line, the establishment of the first segment arc curves can be completed, as well as the remaining arc curves. Finally, a G1 tangent continuous multi-segment arc curve can be achieved with uniqueness (as shown in Figure 4c). The deviation between the original degree-3 curve and final polyarc curve is relatively small (Figure 5).
• Lofting G1 continuous multi-segment arc curves into bending pipes, the interface of adjacent members is parallel to each other and without secondary cut. After curve fitting, the tolerance data, segment length data, and segment quantity data are outputted and analyzed. The length of each arc curve after fitting should not be too short and should be controlled above two times diameter and 1.5 m. If the deviation is large, or segment length is short, or segment quantity is too many, or fitting accuracy or fabrication requirements are not satisfied, it is necessary to return to step 1 and appropriately adjust the allowable deviation for degree reduction of the original curve and repeat subsequent steps (Figure 6).

2.3. NURBS Curve Parametric Fitting Algorithm

A parametric fitting algorithm (Figure 7) is developed using Grasshopper (GH), the generative modeling environment for Rhinoceros (Rhino) based on the above NURBS curve fitting multi-segment arc method. It can automatically divide spatial NURBS curves into several segment arcs that can be used for manufacturing.

3. Post Processing of Structural Member Information and Application of BIM Database Technology

According to the numerous fabrication and installation information of the special-shaped shell pipe structure, a post-processing program for structural member information is developed based on the parametric fitting algorithm in Section 2.3. The algorithm automatically assigns numbers to each member and outputs fabrication information including section size, bending arc length and radius, ratio of curvature radius to steel pipe diameter, as well as hot bending and cold bending fabrication information. Meanwhile, the algorithm also outputs installation information on site including the interface control point number of each member and its installation coordinates. The information is integrated into a BIM database to guide the workshop manufacturing and installation on site of such structures.

3.1. Member Number and Post Processing Program for Bending Manufacture

The bending fabrication technology of arc member is determined by the ratio of the bending arc curvature radius to the pipe diameter. The specific parameters are shown in

Table 1. Bending fabrication technology analysis table.

No.	Ratio of Bending Arc Curvature Radius to Pipe Diameter	Fabrication Technology
1	r/d ≤ 2.7	Steel casting
2	r/d ≤ 30	Hot bending
3	r/d > 30	Cold bending

.

The numbering of the members should consider their position, specification, and processing technology, taking into account the processing and installation characteristics of the special-shaped shell pipe structure. Additionally, geometric elements identification should be incorporated into the digital model.

Finally, the algorithm automatically calculates the segment length, curvature radius of each pipe arc curve, and the value of r/d (the ratio of curvature radius to steel pipe diameter). According to Table 1, it can also output the fabrication process of each bending pipe, member number, and solid model, as shown in Figure 8. The specific algorithm is shown in Figure 9.

3.2. Post Processing Program for Control Points and Line Parameters

Several adjacent members form a transport segment in order to improve assembly efficiency at workshop. Several transport segments are welded together in the ground for reducing high position welding. In order to facilitate the workshop assembly and site installation positioning of bending members, a post-processing program for control points and line parameters is provided. Control points at welding joints are laid out for continuous cross curves in the fitting model. Subsequently, a post-processing program is employed to generate and output control point coordinates in the global erection system and local fabrication system (Figure 10). It is relatively easy for the workshop to mark the positions of four control points on the bending plane for a single bending member, which are all outermost points. Marks are then punched at control points on bending members in the workshop as a mark for workshop assembly and installation on site.

3.3. BIM Database Application

Taking the main application software for construction detailed design, Tekla Structures, as a conversion platform, based on the C# secondary development data conversion program, the integration of geometric model data and Tekla is realized (Figure 11). Then, IFC data are used as conversion text to import a model into the BIM platform [24]. Combing with IoT technology, relevant parties can update member information through the BIM platform client to achieve comprehensive digital management of the project (Figure 12).

4. Position Control of Special-Shaped Shell Pipe Structure

In order to overcome the difficulty in controling a structural position, control technology for special-shaped shell pipe structures is proposed. During the detailed design drawing stage, the structure undergoes pre-camber in three dimensions. By integrating comprehensive construction simulation analysis, both the safety of the entire construction procedure and the consistency between the completed and the design shape can be ensured.

4.1. Structural Pre-Camber

Due to its irregularity, large span, and weak out-of-plane stiffness, large deformations are likely to occur during installation on site. Without reliable control of deformation, the completed structural position will differ from the architectural design and affect subsequent roof structure installation. Therefore, it is necessary to pre-camber the structure for precise control of its completed position [8].

The determination of structural pre-camber values is closely related to construction approaches. Firstly, through construction simulation analysis, deformation values under self-weight and additional dead load can be achieved and superimposed on design structural positions with opposite signs. After re-simulation analysis, the deviation between the completed and design position is calculated. Through repeated iteration, the pre-camber values that satisfy tolerance requirements can be achieved (Figure 13) and the structural position for member fabrication and installation as well. Finally, feedback to the geometry fitting model for three-dimensional coordinate adjustment of nodes and an updated detailed design model and BIM database realize structural pre-camber during the detailed design stage.

4.2. Construction Simulation Analysis

For special-shaped shell pipe structures, during construction procedure, due to the large lifting weight of members, complex structure joints, and member inclination, its structural bearing is relatively complex. A construction sequence has a great impact on bearing and deformation of steel structure in completed state. Moreover, completed structural position has a great impact on subsequent roof structure installation. Therefore, it is necessary to carry out construction simulation analysis (Figure 14) for the installation and unloading process of special-shaped shell pipe structures to ensure structural safety during the construction procedure and estimate the structural position of the completed state. At the same time, it can provide a theoretical basis for structural pre-camber.

5. Digital Construction Technology and Its Application

Combining the above-mentioned technology, a complete set of digital construction technology for special-shaped shell pipe structures is established in Figure 15. Through application of these key technologies in these projects, crucial challenges including member-detailed design and segmentation, fabrication at workshop, member management, installation on site, and accuracy control, were effectively solved. It significantly reduced costs of detailed design, fabrication, and installation technology and management, while ensuring the construction quality of a steel structure, and achieves aesthetic structural appearance. The realization of omnidirectional digital management can be achieved while providing technical support for the completion.

The proposed technology has been successfully applied in large-scale complex projects such as the Haihua Island International Conference Center.

5.1. Engineering Background

The Haihua Island International Conference Center is located in Baimajing Town, Danzhou City, Hainan Province, China. The CH2 unit of the International Conference Center is formed by the convergence of two circular banquet halls and is a bionic curved pipe shell structure. The CH2 unit includes a main entrance, two junction entrances, and two secondary entrances. Each entrance has some petal-dense ribs falling on the arch cantilever ribs. Some entrance arches also need to support the frame columns. The petal appearance is divided into three layers: inner petals, middle petals, and outer petals (Figure 16). The arc radii of the lower column network of each layer of petals are 32/34/36 m, respectively, and the highest point of the petals is about 30 m high. The spacing between the dense ribs of the petals is 1.4~1.6 m. The total steel consumption is about 3195.5 tons, and all steel members are made of Q355B material.

5.2. Application Details and Discussions

Specified application details are as followings:

• The original degree-3 curve is transformed into the final polyarc curve for an outer petal using NURBS curve parametric fitting technology (Figure 17).
• After conducting curve fitting analysis, the maximum deviation between the fitted curve and the original curve measures 54.1 mm, while the average deviation stands at 12.4 mm (Figure 18). These results meet the architectural requirements satisfactorily (Figure 19).
• The Tekla detailed model is efficiently established through the post-processing program of structural member information (Figure 20a). Additionally, a BIM model (Figure 20b) is created via the IFC data interface, enabling comprehensive digital project management on the BIM platform.
• The detailed drawing (Figure 20c) is output to show sectional views of segments indicating relative positions of cross control points at welding joints. It also provides overall coordinates for assembly and installation on site, as well as local coordinates for assembly of cross positioning points at welding joints in the workshop. These coordinates can be used for the installation position of each erection unit on site, ground assembly positioning of each transportation unit on site, and ground assembly positioning of each part in the workshop.
• Taking an outer petal for example, a single NURBS curve with a length of approximately 130 m is composed by more than 50 manufacturing arc members that are about 2.5 m. Every five adjacent members form a transport segment in order to improve assembly efficiency at the workshop (Figure 20d). Every two transport segments are welded together in the ground for reducing high-position welding (Figure 20e).

Despite the promising results, this study has certain limitations. The proposed methods primarily focus on specific types of special-shaped shell pipe structures, which may not be universally applicable to all special-shaped structures with other cross section types. Additionally, the effectiveness of the algorithms and technologies developed may require further empirical validation in more engineering applications. Furthermore, the integration of digital twin technology [25] was not extensively explored in this study. While digital twins could enhance the real-time monitoring and optimization of these structures, the lack of investigation into their application may limit the practical implementation of the proposed methods in dynamic and complex environments.

6. Conclusions

After conducting research on digital construction technology concerning detailed design, fabrication in workshop, on-site installation, and engineering information management for special-shaped shell pipe structures, the following conclusions were derived:

• A parametric fitting algorithm is developed based on the proposed NURBS curve fitting multi-segment arc method. In this method, high-degree curves that are challenging to manufacture are fitted into easily manufacturable multi-segments of equal-curvature arcs. By employing the NURBS curve fitting technique, the architectural appearance can be preserved while simultaneously reducing fabrication difficulty and cost.
• The post-processing of structural member information and the application of BIM database technology are proposed. The algorithm automatically assigns unique identifiers to each member and generates fabrication details such as section size, bending arc length and radius, curvature radius to steel pipe diameter ratio, and bending fabrication information. Additionally, the algorithm provides installation information for on-site operations including interface control point numbers for each member and their corresponding installation position coordinates. Ultimately, a comprehensive BIM database is established to facilitate workshop manufacturing and installation processes while enabling omnidirectional digital project management.
• Structural position control technology for special-shaped shell pipe structures is proposed. Through comprehensive construction simulation analysis, the iterative calculation is performed to determine pre-camber values, enabling the realization of structural pre-camber in the stage of detailed design.
• The proposed digital construction technology can provide complete technical solutions encompassing modeling, detailed design, establishment of member information database, accuracy control of fabrication at the workshop, and installation on-site as well as construction organization management.

Future research should aim to expand the applicability of these technologies to a broader range of structural forms and cross section types. Moreover, the integration of digital twin technology presents an exciting avenue for future exploration. By creating real-time, virtual replicas of physical structures, digital twins can enhance monitoring, predictive maintenance, and decision-making processes throughout the lifecycle of construction projects. This integration could lead to improved efficiency and responsiveness in managing construction operations. Overall, continued innovation in digital construction technology, including digital twins, holds the potential to transform the efficiency and effectiveness of the construction industry.