Digital twinning implementation method based on mechanical properties of cantilever beam under moving load

Abstract

The invention provides a digital twinning implementation method for mechanical properties of a cantilever beam under a moving load, which is characterized in that mechanical influence distribution of different positions of the cantilever beam is calculated in real time under live load (vector) excitation by utilizing strong form weakening of a differential equation of a mathematical model, and comprises the following steps: S1, obtaining a mechanical component constraint model; obtaining a position function model according to boundary conditions; s2, separating the position equation under the weak formalization; s3, separating the load equation under the weak formalization; and S4, carrying out coupling operation on the position function and the load function which are obtained through order reduction. According to the method, the mechanical distribution condition of the cantilever beam under excitation of different loads can be observed in real time, the calculation speed is greatly increased through model order reduction, and high calculation precision is kept.

Description

Technical Field

[0001] The present invention belongs to the application of solving the real-time calculation problem of the force conditions (influence lines) at various positions of a cantilever beam under a moving load by using the truncation and approximation of separable functions, especially in the case where small time steps are required, with higher calculation efficiency and accuracy. Background Art

[0002] With the continuous development and growth of science and technology, the demand for high-dimensional real-time calculation is continuously increasing, and the demand for the state monitoring of beams and other engineering stress components emerges as the times require, and the digital twin demands for bridges and steel cables are growing day by day. With the development of computer-related technologies and the improvement of numerical calculation methods related to the intrinsic generalized decomposition, using the variational formula, the domain is discretized by the finite element method, and it is assumed that its solution can be approximated as a single function representation, and an iterative algorithm is used to find its solution.

[0003] The purpose of the present invention is to reduce the order of the model of the influence line of a high-order complex three-dimensional mechanical field on a cantilever beam based on the finite element theory to improve its operation speed and efficiency, and obtain its high-precision solution. Summary of the Invention

[0004] The present invention provides a method for solving the calculation of the influence line of a cantilever beam under a moving load. Using the finite element theory and programming through Matlab, it includes the following steps:

[0005] Step 1: Weakly formulate the strong-form problem;

[0006] According to the actual application scenario, multiply the strong-form problem by a test function and integrate it over its boundary part to obtain the weak form of the problem.

[0007] Step 2: Reduce the order of the load function.

[0008] Assume the modulus value of the load and specify its direction (assume it acts along the vertical axis), and approximate the load function by a truncation function, approximated as the product of two functions as follows f and g are respectively the j-th component of the approximate reduction of the load and the boundary position.

[0009] Step 3: Iterate the position function U(X, Y, Z) using the test function and obtain its solution;

[0010] According to the approximation of the obtained load function and the weak form of the position function, and substitute the test function. Iteratively obtain the test function value based on the known conditions, and substitute it into the position function to obtain the solution sought Detailed Description of the Invention

[0011] The following further elaborates the specific implementation manners of the present invention in conjunction with the drawings and examples

[0012] Based on the finite element theory and supported by the Matlab programming software, the present invention performs real-time reduced-order calculation on the live load influence line of mechanical components. Model reduction is carried out for high-dimensional complex functions, approximated by multiplying two functions of different dimensions, which greatly reduces the calculation time and complexity, providing the possibility for the realization of digital twin. The experimental results show that this method has quite high accuracy.

[0013] For the analysis of the load influence line of mechanical components, the following specific steps are included:

[0014] Step 1: Obtain the constraint model of the mechanical component and construct its function model according to its boundary conditions;

[0015] Obtain the function model of the cantilever beam, multiply its function by the test function, and perform integration on its boundary conditions to obtain the weak form of the problem. The position function and the load function are approximated as two multiplied function forms using the truncation function.

[0016] Step 2: Based on the L.H.S equation in the weak form, separate the position equation

[0017] Extract the node value vector in the test function integration. The original integral formula obtains the position function in the form of the multiplication of the stiffness matrix based on the spatial coordinates and the one-dimensional discretized mass matrix based on the load position.

[0018] Step 3: Based on the R.H.S equation in the weak form, separate the load equation

[0019] Perform similar processing on the RHS term in the weak form. Since the known condition is the load position coordinate, the original load function can obtain the load function in the form of the multiplication of two terms, namely the spatial variable of the node value decomposed based on the load source term and the load direction.

[0020] Step 4: Couple and iterate the obtained position function and load function to obtain the result

[0021] Couple the stiffness matrix based on the spatial coordinates and the spatial variable of the node value decomposed based on the load source term, as well as the one-dimensional discretized mass matrix based on the load position and the load direction respectively. Calculate and solve the two coupled variables to obtain the influence line of the original cantilever beam. From the above examples, it can be seen that the error value between the calculation result using this method and the actual measurement value is very small and the value is accurate; the error between the reduced-order calculation value of the model and the actual measurement value can meet the engineering requirements and is within the allowable range. It proves the rationality of the present invention in the model and mechanical field settings, can calculate the influence line of the cantilever beam under live load, and proves the feasibility of this method for numerical calculation.

[0022] Invention effect

[0023] The present invention overcomes the deficiencies of the prior art, completes the calculation problem of the real-time influence line of a cantilever beam under live loads, and ensures the accuracy of its calculation results. It provides a reference for the mechanical distribution when loads with different directions, sizes, and positions act on a mechanical component.

[0024] It should be emphasized that the embodiments described in the present invention are illustrative rather than restrictive. Therefore, the present invention includes, but is not limited to, the embodiments described in the specific implementation manners. Any other implementation manners obtained by those skilled in the art based on the technical solutions of the present invention also fall within the scope of protection of the present invention. Description of the Drawings

[0025] Figure 1 Schematic diagram of live load acting on a cantilever beam

[0026] Figure 2 Mesh diagram of the beam dissection

[0027] Figure 3 Distribution diagram of mechanical influence caused by taking the case of live load acting on the upper side of the beam as an example

[0028] Figure 4 Application diagram of the mechanical influence distribution caused by taking the case of live load acting on the upper side of the beam as an example.

Claims

1. A digital twin implementation method for the mechanical properties of a cantilever beam under moving loads, which uses the decomposition of its mathematical model to calculate the mechanical influence distribution at different positions of the cantilever beam in real time. The method includes the following steps: Step 1: Weakly formulate the strong-form problem. According to the actual application scenario, multiply the strong-form problem by a test function and integrate it over its boundary part to obtain the weak form of the problem. Step 2: Reduce the order of the load function. Assume the magnitude of the load and specify its direction (assuming it acts along the vertical axis), and approximate the load function with a truncation function, approximated in the form of the product of two functions as follows f and g are respectively the j-th component of the approximate reduction of the load and the boundary position. Step 3: Iterate the position function U(X, Y, Z) using the test function and obtain its solution. Based on the approximation of the obtained load function and the weak form of the position function, substitute them into the test function. Iteratively obtain the test function value according to the known conditions and substitute it into the position function to obtain the solution.

2. A digital twin implementation calculation method for the mechanical properties of a cantilever beam under moving loads as described in claim 1. Wherein, The mechanical component in Step 1 is a cantilever beam.

3. A digital twin implementation calculation method for the mechanical properties of a cantilever beam under moving loads as described in claim 1. Wherein, The cantilever beam model in Step 1 is a cantilever beam structure with a length of 3 m and a width of 1 m, and the calculation grid step size is 0.1 m.

4. A digital twin implementation calculation method for the mechanical behavior of a cantilever beam under moving loads as described in claim 1. Wherein, The Young's modulus of the material is E = 1000 Pa, and the Poisson's ratio is 0.3.

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