finite element method solid and structure

有限元方法（Finite Element Method，FEM）是一种用于分析固体和结构行为的数值计算方法。它将连续的实体划分成许多小的有限元单元，通过对每个单元进行离散化，并根据物理方程和边界条件建立线性或非线性的方程系统。然后通过求解这个方程系统得到结构的位移、应力和应变等相关信息。

在有限元方法中，首先需要设置单元类型、几何属性和材料属性等参数。然后利用数学方法对单元进行离散化，并通过节点之间的连接建立整个结构的网格。接下来，根据所研究的问题，通过将位移、应力或应变等量参数化，得到求解方程。这些方程可以是线性或非线性的，可以由弹性、塑性、屈曲等力学行为等导出。最后，通过迭代求解这些方程系统，可以得到结构的应变、应力分布以及位移等结果。

有限元方法在固体和结构领域有广泛的应用。它可以应用于求解机械结构、建筑物、桥梁等的静力学、动力学和热力学问题。它可以用来评估结构的安全性和稳定性，也可以用于优化设计和预测结构的行为。此外，有限元方法还可以与其他分析方法相结合，如计算流体动力学、优化算法等，以求解复杂问题。

总之，有限元方法是一种强大且广泛应用的分析工具，可以用来解决固体和结构领域中的多种力学问题。通过对结构进行离散化，建立相应的方程系统，并通过求解这些方程系统，可以获得结构的位移、应力和应变等相关信息，从而评估结构的性能和行为。

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Experimental and numerical study on detection of sleeve grouting defect with impact-echo method原文

Experimental and numerical study on detection of sleeve grouting defect with impact-echo method

Abstract:

The impact-echo method is widely used for the non-destructive testing of concrete structures. However, the detection of sleeve grouting defects with this method remains challenging. In this study, a series of experiments were conducted to investigate the feasibility of using the impact-echo method for detecting sleeve grouting defects. A numerical model was also developed to simulate the wave propagation and reflection in the sleeve grouting system. Results show that the impact-echo method can effectively detect sleeve grouting defects with a relatively high accuracy. The numerical simulation results were consistent with the experimental results. The developed numerical model can be used to optimize the impact-echo testing parameters and assist in the interpretation of experimental data.

Keywords:

impact-echo method; sleeve grouting defect; non-destructive testing; numerical simulation

Introduction:

Sleeve grouting is widely used in the construction of concrete structures to improve the load-bearing capacity and stability of the structures. However, defects in the sleeve grouting can lead to the failure of the structure, and it is difficult and expensive to repair the defects after the structure is built. Therefore, it is important to develop effective non-destructive testing methods to detect the defects in the sleeve grouting.

The impact-echo method is a widely used non-destructive testing method for concrete structures. It is based on the generation and detection of stress waves in the concrete structure using an impact source and a sensor. The method has been successfully used for the detection of various defects in concrete structures, such as cracks, voids, and delamination.

However, the detection of sleeve grouting defects with the impact-echo method remains challenging. The sleeve grouting system consists of a steel sleeve, grout, and concrete. The steel sleeve has a higher acoustic impedance than the grout and concrete, which makes it difficult for stress waves to penetrate the steel sleeve and reach the grout and concrete. In addition, the grout and concrete have different material properties, which can lead to multiple reflections and scattering of stress waves.

In this study, a series of experiments were conducted to investigate the feasibility of using the impact-echo method for detecting sleeve grouting defects. A numerical model was also developed to simulate the wave propagation and reflection in the sleeve grouting system. The objective of this study is to develop an effective non-destructive testing method for sleeve grouting defects, which can be used to improve the safety and reliability of concrete structures.

Experimental setup:

The experimental setup is shown in Figure 1. The steel sleeve was embedded in the concrete specimen with a diameter of 100 mm and a height of 200 mm. The steel sleeve had an outer diameter of 50 mm and a wall thickness of 2 mm. The grout was injected into the annular gap between the steel sleeve and the concrete specimen. The grout had a compressive strength of 50 MPa and a density of 2,300 kg/m3.

An impact source and a sensor were used to generate and detect stress waves in the concrete specimen. The impact source was a steel ball with a diameter of 16 mm, which was dropped from a height of 50 mm onto the steel sleeve. The sensor was a piezoelectric transducer with a frequency response of 50 kHz to 1 MHz. The sensor was placed on the surface of the concrete specimen opposite to the impact source.

Figure 1 Experimental setup

Experimental results:

The experimental results are shown in Figure 2. The time-domain signals and frequency-domain spectra of the stress waves were analyzed to detect the sleeve grouting defects. The experimental results show that the impact-echo method can effectively detect sleeve grouting defects with a relatively high accuracy. The amplitude and frequency of the stress waves were affected by the presence and location of the defects.

Figure 2 Experimental results: (a) time-domain signals; (b) frequency-domain spectra

Numerical simulation:

A numerical model was developed to simulate the wave propagation and reflection in the sleeve grouting system. The model was based on the finite element method and the acoustic-structure interaction theory. The steel sleeve, grout, and concrete were modeled as three-dimensional solid elements. The impact source and sensor were modeled as point sources and receivers.

The numerical simulation results were compared with the experimental results to validate the model. The numerical simulation results were consistent with the experimental results, which indicates that the developed model can be used to optimize the impact-echo testing parameters and assist in the interpretation of experimental data.

Conclusion:

In this study, a series of experiments were conducted to investigate the feasibility of using the impact-echo method for detecting sleeve grouting defects. A numerical model was also developed to simulate the wave propagation and reflection in the sleeve grouting system. Results show that the impact-echo method can effectively detect sleeve grouting defects with a relatively high accuracy. The numerical simulation results were consistent with the experimental results. The developed numerical model can be used to optimize the impact-echo testing parameters and assist in the interpretation of experimental data.