The finite element (FiniteElement) method is a modern calculation method developed rapidly with the development of electronic computers, which is widely used in machinery, structure, aerospace and other fields, and has been deeply promoted in the field of shelves, and is an indispensable important tool for the structural design of steel shelves. For finite element analysis, the establishment of the model and the selection of the load are the core steps, and the following two core points are described separately.

The finite element (FiniteElement) method is a modern calculation method that has developed rapidly with the development of electronic computers, and is widely used in various fields such as machinery, structure, aerospace, etc.ShelfThe field has been deeply promoted and is an indispensable tool for the design of steel shelf structures. For finite element analysis, the establishment of the model and the selection of the load are the core steps, and the following two core points are described separately.

1. model simplification

Steel shelf is a special steel structure, which is composed of a large number of repeated and regular columns and beams. The number of bars far exceeds that of ordinary steel structures. If the traditional modeling method is followed, the number of nodes and units will be too large, which will seriously affect the calculation efficiency. Considering the regularity of shelf structure, it is very necessary to simplify it, but how to simplify it becomes the key to finite element application.

The actual structure of the shelf is abstracted into a parametric calculation model, and the simplification process of transforming the calculation model into a finite element model mainly involves three types of simplification, namely, the simplification of the shelf structure, the simplification of the unit type and the simplification of the node.

1. Simplified shelf structure

The overall finite element model of the shelf should be simplified as a spatial three-dimensional frame model. The natural nodes connected by components are taken as structural model nodes, and adjacent nodes form units.

A. for ordinary shelves without vertical tie rod devices, such as ordinary beam type shelves, shelf type, ordinary shuttle type and other simple structure shelves, generally take no less than 5 rows of shelves as the research object for modeling.

B. For shelves with regular structure and continuous stress, such as ordinary ASRS beam type shelves, bull leg type shelves, multi-wear and four-way shuttle car shelves, etc., it is appropriate to divide according to the proportion of the tie rod system, and select one or two groups of vertical tension for modeling by using the average tie rod method. For example, for a beam type shelf, 30 rows of shelves have 4 sets of vertical tie rods, and each set of vertical tie rods controls about 7.5 rows of shelves. Therefore, 7 rows of shelves can be used for modeling. The model includes a set of vertical tie rod system, or 15 rows of shelves can be used as a simplified model, and the structure of 2 sets of vertical tie rods can be used as a simplified model. Such simplification can achieve a simple and accurate balance between the simple model and the real model.

c. For large-scale storage racks, because the shelf force is more complex, and the force is discontinuous, according to the above method to take the local three-dimensional unit model can not reflect the force of the entire shelf, at this time the model can be simplified to two directions of the overall plane model for calculation. In a single plane, the model can completely reflect the overall shelf structure.

d. For very large structures, the connection method is more complex, in order to simplify the model, some of the combined components can be replaced by a single component to replace an entire combination, to simplify the entire model to improve modeling efficiency. For example, a similar method is adopted along the roadway direction in which the upper warehouse and frame are integrated, and several rows of shelf pieces are simplified into an equivalent rod.

2. Unit simplification

Shelf structure unit can be simply divided into two categories: rod unit and beam unit, for the two ends of the hinged, basically only by the axial force of the component, can be simplified as a rod unit, can greatly reduce the amount of computer calculation.

3. Node simplification

Another part that needs to be perfected after the establishment of the overall model is the processing of node connection methods. For nodes, they are mainly divided into hinged, rigid and semi-rigid connections. Both ends of the rod unit are regarded as hinged, so the nodes that need to be dealt with are mainly the connection nodes between the beam units, the most important of which are two kinds of nodes, ground nodes and beam-column nodes.

a. Foot node

The anchor node is the connection node between the column and the ground. We will simplify the model according to different anchor forms. There are three main anchor models used in the general shelf design:

(1) Approximate rigid foundation model, that is, it is considered that the foundation and the shelf are rigidly connected. In fact, the foundation mode in reality is difficult to reach the degree of rigid connection, which is semi-rigid connection. However, for some special forms, it is closer to the fixed connection, and the calculation can be simplified approximately according to the fixed connection consideration. For example, in the form of embedded foundation, the column is fixed on a thicker embedded plate by welding, and the embedded plate, in this case, it can be approximated as a fixed column foot.

(2) Semi-rigid grounding foot model, that is, it is believed that the foot will deform under the action of load, and the influence of deformation on the shelf structure cannot be ignored. At this time, the stiffness of semi-rigid joints needs to be considered. The stiffness needs to be obtained by making the M-θ curve of the foot through tests in advance, and then the stiffness value is brought into the model for calculation, generally, the connecting column foot form of the most commonly used twin-screw adjusting cement pier in the industry can be regarded as a semi-rigid connection along the direction of the roadway.

(3) Hinged anchor, the anchor does not limit any rotational freedom. In general, when the shelf anchor is connected by a single screw, we can regard it as a two-way hinge for simulation calculation in the model. In addition, when the twin-screw connection is adopted, the twin-screw is arranged along the direction of the roadway, and the vertical direction of the roadway is actually still a single screw, so the vertical direction of the roadway should still be regarded as articulated.

B. Beam-column joints
For combined shelves, there are two main ways to deal:

(1) Semi-rigid connection:

When the hanging piece is used for installation between the beam and the column, several hanging claws are embedded in the column, and the beam and the column itself are thin-walled structures, which will produce certain elastic deformation after being stressed, allowing certain rotation between the beam and the column. This connection is a typical semi-rigid connection.

The semi-rigid characteristics of beam-column joints are the most typical characteristics of shelf structures. All qualified shelf manufacturers should conduct M-θ corner tests on them to obtain the stiffness values of different columns and beam connection nodes, and then apply them in calculations or finite element simulations to simulate the actual situation more accurately.

(2) Articulation:

There is also a connection method in the shelf. When using C- type or ∑-type continuous beams, the beams and columns are fixed by bolts, and the bolts are located within the section of the beam. Although the beams in this form are semi-rigid connections, due to their small stiffness, they can generally be considered hinged in application and calculated as simply supported beams.

The use of semi-rigid stiffness value is essential for the shelf without vertical support and is a necessary factor to maintain the stability of the shelf. However, for complex structures, in the shelf structure with a large number of vertical supports, or when designing to consider higher shelf safety, the beam-column joints can be simplified as hinges during modeling. Through a large number of comparative simulation calculations, we think it is feasible.

2. load

A. add shelf dead weight, structural analysis software will automatically generate shelf dead weight according to cross-sectional properties and material density, etc., but when there are fixed equipment in the shelf, such as fans, fire pipes, etc., the weight should also be included in the shelf dead weight, and the load needs to be manually added at the corresponding position. The library-frame integration project also needs to consider the weight of roof panels, wall panels, auxiliary fixtures, etc.
B. Add live load, mainly cargo load, and add corresponding point load or uniform load according to the force form of the beam. For projects such as the integration of storage and frame, roof live load should also be considered.
c. Add imaginary load, generally in accordance with the weight of the goods to add 1/250.
d. Add all kinds of impact load, including the impact load of the goods placed, the impact load of the stacker operation, etc;
e. Add the corresponding earthquake action, wind load and snow load according to local specifications (indoor shelves do not need to consider wind load and snow load), and the seismic design is generally designed by the vibration mode decomposition response spectrum method.
F. according to the local specifications, load combination, and then post-processing, finite element software can get the force of each rod and node, and check the shelf.

Simple and effective finite element model allows us to deal with the complex shelf structure, more quickly and more accurately to get the calculation results of the shelf, so that we check and improve the efficiency of the shelf structure greatly improved. With the development of computer calculation, the operation of finite element software is becoming more and more simple, the function is becoming more and more powerful, and the calculation efficiency is getting higher and higher, which has become an indispensable part of shelf design.