Mesh and shell structure shape finding analysis and case appreciation

1 What is mesh shell

Mesh shell is a kind of space rod system structure similar to flat plate rack, the system is based on rods, according to a certain law of the grid, according to the shell structural arrangement of the space frame, which has both the nature of the rod system and the shell. Its force transmission is mainly characterized by point-by-point force transmission through tension, pressure or shear force in two directions in the shell. This structure is a kind of space structure which has attracted much attention at home and abroad and has a broad development prospect. The net-shell structure includes single-layer net-shell structure, prestressed net-shell structure, plate cone net-shell structure, rib-ring type cable bearing net-shell structure, single-layer forked tube net-shell structure, etc.

2 History of the development of mesh shells

The prototype of mesh shell structure–dome structure. In the course of development of human society, large-span space structure is often the dream and goal pursued by architects. Among them, the development of mesh shell structure has gone through a long historical evolution process. Ancient human beings, through detailed observation, utilized the principle of bionic, in order to have a better living space, often using tree branches as skeleton and straw as skin to imitate such as eggshells, bird’s heads, and caves, to build dome structures, i.e., the initial tents. With the development of building materials, the dome of stone, later gradually replaced by masonry. The span of the dome is generally small, at about 30m ~ 40m, of which the Roman Pantheon built in 120 ~ 124 AD is a typical representative of the early dome. In the 19th century, the application of iron for the development of the dome opened a new era, the emergence of modern reinforced concrete structure theory and application of the new field of large-span thin-shell dome. 1922 in Jena, Germany, built the first civil engineering history of reinforced concrete thin-shell structure—Jena Planetarium.

the Pantheon in Rome

Jena Planetarium

With the emergence and application of lightweight and high-strength materials such as iron, steel and aluminum alloys, imaginative engineers began to use a variety of rod forms for dome structures. Recognized as the “father of dome structure” – German engineer Schwedler played a key role in the birth and development of the dome mesh shell, he put forward a new construction pattern on the basis of thin-shelled dome, i.e., the dome shell surface is divided into the longitudinal ribs and latitudinal horizontal loops, and connected together, and In each trapezoidal grid and then divided into two or four triangles with diagonal rods, so that the distribution of internal forces on the surface of the dome will be more uniform, and the weight of the structure itself will be further reduced, so that it can span a larger space. Such a dome structure is actually a real mesh-shell structure, i.e., a regular arrangement of roughly the same mesh or smaller-sized cells along a certain surface, thus composing a spatial rod system structure.

Schwedler Mesh Shells

3 Mesh and shell structure to find the shape

After looking at some building cases of mesh and shell structure, we talk about mesh and shell structure shape finding from the structural aspect. Regarding structural shape finding, there are a lot of contents available on the Internet, and the mainstream ones are usually divided into three kinds: force density method, dynamic relaxation method, and nonlinear finite element method. About these three methods, I usually prefer to use the third method, namely the nonlinear finite element method, the following to focus on the nonlinear finite element method.

Nonlinear finite element method of the basic principle is simply the use of inverse hanging way to complete the shape, text description is too boring, words do not say directly on the example. If the building gives you a roof skin, such as a circular skin, see the figure below.

building skin

We assume that it is surrounded by concrete roof supports and that the entire roof is a circular mesh shell structure. We import it into ABAQUS, and since the roof is usually subjected to uniform vertical face loads, we apply reverse face loads to it using a reverse-hanging scheme.

abaqus finite element modeling

We use a 5mm thick steel plate to simulate the shell so that its bending stiffness is negligible and there is only tensile stress and no bending moment in the shell. This way we find a shape where there is only pure pressure in the shell under uniform pressure and no bending moment due to the span.

Shell structure is thin, so the overall bending performance is very poor, and usually it is used in larger span space structure, so we need to find the shape to solve the bending moment brought about by the span, which is also one of the purposes of finding the shape. The next step is to import the shell shape calculated by ABAQUS into Rhinoceros, and then lay out the shell rod on the plane, project it onto the surface, and the space mesh shell structure formed is the final structural model we need, and the whole process is relatively simple, so we won’t demonstrate it in detail.

search results

Actual force diagram of the structure

Summary

The mesh shell structure has its unique beautiful shape, simple, with organization, extremely slim, so that people look pleasing to the eye, but as a structural engineer encountered large-span mesh shell structure should be from various aspects of its calculation and analysis, its initial defects, overall stability, shell foot support thrust, construction simulation analysis, etc. are all need to pay attention to the place. However, as the calculation software becomes more and more mature, the mesh shell structure is bound to get more applications in the future projects.