CN-122021196-A - Prestress beam simulation method based on incomplete bonding theory and vector finite element

CN122021196ACN 122021196 ACN122021196 ACN 122021196ACN-122021196-A

Abstract

The invention discloses a prestress beam simulation method based on an incomplete bonding theory and vector finite elements, which comprises the steps of calculating mechanical responses of prestress beam sections under different loading actions based on an incomplete bonding theory model to construct a bending moment-corner relation, dispersing a prestress beam structure of the prestress beam sections into a plurality of mass particles by adopting a vector finite element method, connecting the mass particles by a mass-free beam unit to construct a global structure analysis model, taking the bending moment-corner relation as a force-deformation relation of the mass-free beam unit in the global structure analysis model, calculating displacement responses of the mass particles in the global structure analysis model, updating internal force according to deformation and the bending moment-corner relation of the mass-free beam unit in the calculation process, and outputting simulation results of the prestress beam structure. The method provided by the invention can accurately simulate the complete stress behavior of the beam from elasticity, cracking and yielding to limit damage, and provides data support for subsequent research.

Inventors

FENG QIAN
TIAN MAOLIN
ZHANG HONGMEI
DUAN YUANFENG

Assignees

浙江大学

Dates

Publication Date: 20260512
Application Date: 20260413

Claims (8)

1. The prestress beam simulation method based on the incomplete bonding theory and the vector finite element is characterized by comprising the following steps of: Calculating mechanical responses of the prestressed beam section under different loads based on the incomplete bonding theoretical model so as to construct a bending moment-rotation angle relation of the prestressed beam section when bearing the load; dispersing a prestress beam structure with a prestress beam section into a plurality of mass points by adopting a vector finite element method, and connecting the mass points by using a non-mass beam unit to construct a global structure analysis model; And taking the bending moment-corner relationship as a force-deformation relationship of the mass-free beam unit in the global structure analysis model, calculating displacement response of each mass particle in the global structure analysis model through explicit time integration, updating internal force according to the deformation of the mass-free beam unit and the bending moment-corner relationship in the calculation process until the termination condition is met, and outputting a simulation result of the prestress beam structure.
2. The method for simulating a prestressed beam based on the incomplete bonding theory and vector finite element according to claim 1, wherein the bending moment-rotation angle relation comprises a before-section cracking and a after-section cracking; Before the section cracks, adopting linear strain distribution to calculate the strain of the concrete, the non-prestressed reinforcement and the prestressed reinforcement in the direction along the height of the beam, calculating the stress at the position corresponding to the height of the beam according to the stress-strain relation of the material, and then solving the position of a neutral shaft through the force balance iteration in the section so as to calculate the bending moment-rotation angle relation under the loaded state; After the section is cracked, the pre-constructed tension-slip relation is adopted to match with the slip quantity at the section of the crack, the tension of the corresponding steel bar and the prestress steel bar is calculated, and then the position of the neutral axis is solved through the force balance iteration in the section, so that the bending moment-rotation angle relation under the loaded state is calculated.
3. The method for simulating a prestressed beam based on the incomplete bonding theory and vector finite elements according to claim 2, wherein the tension-slip relationship is obtained by performing a tensile rigidification analysis on a concrete prism wrapping a reinforcing steel bar or a prestressed steel bar.
4. The prestress beam simulation method based on the incomplete bonding theory and the vector finite element according to claim 2, wherein the process of solving the neutral axis position through the force balance iteration in the section is as follows: Giving a section rotation angle and estimating an initial value of the depth of the neutralization shaft; judging whether the axial force of the section is balanced or not based on the stress or the tension obtained by calculation, if not, adjusting an initial value, and recalculating the corresponding stress or tension; if the balance is judged, calculating the sum of the moment of the stress or the tension on the cross section neutralization shaft so as to obtain the resisting bending moment corresponding to the cross section rotation angle; The above process is repeated to construct a bending moment-rotation angle relationship.
5. The prestress beam simulation method based on the incomplete bonding theory and the vector finite element according to claim 1, wherein a virtual inverse motion method is adopted to decouple the total displacement of the mass-free beam unit in the current time step into rigid motion and pure deformation, and the pure deformation is extracted to calculate the corresponding internal force in the deformation and bending moment-rotation angle relation.
6. The method of claim 1, wherein the motion constraint is performed by newton's second law for a plurality of mass points in the global structural analysis model.
7. The method for simulating the prestress beam based on the incomplete bonding theory and the vector finite element according to claim 1, wherein the explicit time integration is performed by adopting a central difference method.
8. The method for simulating a prestressed beam based on the incomplete bonding theory and the vector finite element according to claim 1, wherein the termination condition includes a preset calculation time or loading condition being satisfied.

Description

Prestress beam simulation method based on incomplete bonding theory and vector finite element Technical Field The invention belongs to the field of structural engineering and computational mechanics, and particularly relates to a prestress beam simulation method based on a non-complete bonding theory and vector finite elements. Background The bonding sliding behavior of the steel bars/prestressed tendons and concrete of the prestressed concrete beam under the load effect and the influence of the reduced bonding force of materials on the overall stress behavior of the structure are accurately simulated, and particularly, the degradation of the rigidity of the beam after cracking, the development of cracks of the concrete and the reduction of the ultimate bearing capacity of the beam are very important for structural safety evaluation and design optimization. Traditional analysis methods, such as section analysis based on bending moment-curvature (M- χ) relationship, are the basis of design specifications in various countries. The method is based on the assumption of a flat section, and can provide more accurate results before the concrete cracks. However, for stress behavior after cracking, this approach relies heavily on empirical, effective flexural stiffness formulas to simulate, for example, the Branson formula. More importantly, the M- χ method cannot take into account the bond-slip (bond-slip) effect between the steel bar and the concrete by mechanical mechanisms, and thus cannot truly reflect the phenomenon of "stretch-rigidification" (Tension-STIFFENING) caused by bond-slip. In terms of numerical modeling, conventional Finite Element (FE) methods, while capable of handling complex geometries and material nonlinearities, have limitations in practical engineering applications. First, the accuracy of finite element analysis is highly dependent on modeling techniques, such as selection of cell type, grid density, and boundary conditions. To obtain sufficient accuracy, a high density grid is often required, which results in a huge computational effort, especially in nonlinear iterative analysis. Second, conventional finite element methods are also difficult to directly simulate the stretch stiffening effect by simple constitutive models, often requiring the introduction of empirical adjustments. Vector finite element method (Vector Form INTRINSIC FINITE ELEMENT, VFIFE) is an emerging numerical method that based on the principle of Vector mechanics, discretizes a structure into a particle system, describing the behavior of the structure by solving the motion equation of the particles. VFIFE shows unique advantages in dealing with strong non-linear problems such as large deformation, cracking, collision, etc. However, how to accurately implant complicated section mechanical behaviors (such as bond slip and stretch rigidification) of a prestressed concrete beam into VFIFE frames after cracking is a difficult problem faced by the prior art. Patent document CN120163009A discloses a prestress beam simulation method, a system and equipment based on vector finite element, the method comprises the steps of establishing a prestress beam numerical model by adopting a vector finite element method, dispersing the prestress beam numerical model into a plurality of nodes and a plurality of prestress beam units, calculating a rigidity matrix of each prestress beam unit, determining a control equation of each node based on the rigidity matrix, solving the control equation of each node by adopting a central difference method, and updating the state of each node according to a solving result to complete the simulation of the prestress beam. The patent document CN121031238A discloses a construction method of a coefficient prediction model, a coefficient prediction method and a storage medium, wherein the construction method comprises the steps of modeling a bridge prestress beam by adopting finite element numerical software and simulating a tensioning process, constructing a bridge parameter coefficient array, dividing the bridge parameter coefficient array into a training data set and a verification data set, carrying out data standardization and tensor data conversion, constructing a data loader, constructing a full-connection multi-layer multi-task neural network based on the data loader, arranging a normalizer, a forward propagation function, a loss function, a learning rate scheduler and an optimizer, carrying out model training, packaging the prediction function, and integrating the normalizer and the trained prediction model. Disclosure of Invention The invention aims to provide a prestress beam simulation method based on a non-complete bonding theory and vector finite elements, which can overcome the dependence of a traditional method on an empirical formula and accurately simulate the complete stress behavior of a beam from elasticity, cracking and yielding to limit damage, in particular to the stretching rigidifica