基于无网格自然单元法的超长桩水平承载力研究
发布时间：2018-08-07 11:43
【摘要】：随着科学的发展，数值方法在工程上的应用越来越广泛，其中有限元方法在工程上的应用最广。但有限元在处理大变形的非线性力学问题中存在网格畸变或缠结等不足，同时有限元在求解液体振动、裂纹扩展、材料相变和成形等不定边界或可动边界问题时，需要重新划分网格，而新旧网格之间物理量转换将产生新的误差。因此，无网格方法应运而生。无网格方法不需要借助任何单元，直接利用节点构造插值函数，避免了有限元方法的以上缺陷。在多种无网格方法中自然单元法以其独特的优势获得了快速的发展。 当前，超长桩大量应用于超高层建筑、大跨桥梁和深水港口工程中。然而，超长桩现阶段的研究相对滞后，工程中仍按普通桩理论进行设计，现有理论及分析模型不能充分考虑分层土特性或横纵荷载共同作用的影响，也无法很好地反映超长桩的承载性状。特别在港口工程中，超长桩通常承受很大的水平荷载，并且在横纵荷载共同作用下，往往发生大变形，而传统有限元方法在模拟计算大变形的超长桩和土体的相互作用时存在网格畸变或缠结等问题。 针对以上问题本文在自然单元法理论基础上进一步改进了插值函数，，并将其应用到成层地基中超长桩水平承载力问题上。主要的研究工作及创新点如下： 1、改进了自然单元法的插值函数，编制三维无网格自然单元法计算程序。本文采用的是Voronoi图中二阶结构的边元素作为插值变量，大幅度提高了计算效率。无网格程序不需要借助任何单元，直接利用节点构造插值函数，避免了有限元中的网格畸变等问题，弥补了有限元在处理大变形、非线性力学等问题中存在的明显缺陷，具有较高的工程实用价值和广阔的应用前景。将程序计算结果与解析解及有限元计算结果相比较，验证了本程序的正确性和合理性。 2、基于变分原理计入横纵向荷载共同作用下超长桩的P-Δ效应，推导出单元刚度修正矩阵。针对横纵向荷载共同作用下超长桩的大变形问题，建立考虑非线性大变形的无网格自然单元法计算方法。通过对实例的计算分析，验证了该方法的正确性和合理性，得到P-Δ效应特征。结果表明：由于P-Δ效应，桩的位移响应与荷载为非线性关系。当地基土质较差，桩自由长度较大时，P-Δ效应对桩身位移和内力的影响不可忽略。本方法为计算时考虑P-Δ效应提供了一种简便易行的方法，在工程设计和施工中具有一定的价值。 3、基于无网格自然单元法计算并分析了荷载大小、加载顺序、长径比、桩顶约束条件、水平荷载作用位置、桩土相对刚度比和荷载分布形式等诸多参数对超长桩水平承载力的影响，并得出相关结论。 4、当层状地基中采用p-y曲线法模拟桩周土非线性特性时，桩周土水平位移的计算误差随荷载增大而增大。针对该问题本文采用层状弹性体系理论考虑土体纵向连续性，并利用层状各向同性体的研究方法，建立了适用于桩周层状地基的水平位移系数传递矩阵解法。根据有限单元等效载荷的计算原理，推导出水平位移系数矩阵，并给出外荷载较大时，p-y曲线法桩周土体水平位移的修正式。根据所建立的模型编制程序，对某三层地基土水平位移系数矩阵进行了计算和分析，验证了该方法的正确性和合理性。由于计入了土体的纵向连续性，本文方法所得的水平位移影响系数曲线在荷载作用点的及其邻近区域较Mindlin解的曲线更平滑，位移小于Mindlin解的结果。这表明当土层间性质差异较大时，本文方法能更好地体现层状土体实际分布差异的影响和临近土层间的相互作用。
[Abstract]:With the development of science, the application of numerical methods to engineering is becoming more and more extensive, and the finite element method is the most widely used in engineering. However, the finite element method has the defects of grid distortion or entanglement in the nonlinear mechanical problems dealing with large deformation. At the same time, the finite element method is used to solve the liquid vibration, crack propagation, material transformation and forming. In the case of boundary or movable boundary, it is necessary to remesh the grid, and the physical quantity conversion between the old and the old grids will produce new errors. Therefore, the meshless method emerges as the times require. The unit method has gained rapid development with its unique advantages.
At present, super long piles are widely used in super high rise buildings, large span bridges and deepwater port engineering. However, the research of super long piles is relatively lagging at the present stage. In the project, the design is still in accordance with the common pile theory. The existing theory and analysis model can not fully consider the effects of the characteristics of layered soil or vertical and longitudinal loads. Bearing behavior of long piles, especially in port engineering, super long piles usually bear large horizontal loads, and large deformation often occurs under the joint action of transverse and longitudinal loads, and the traditional finite element method has the problems of lattice distortion or entanglement in the interaction of large deformation super long piles and soil.
In this paper, the interpolation function is further improved on the basis of the theory of natural element method, and applied to the horizontal bearing capacity of the super long pile in the layered foundation. The main research work and innovation points are as follows:
1, the interpolation function of the natural element method is improved and the three-dimensional meshless natural element method is developed. This paper uses the edge elements of the two order structure in the Voronoi diagram as the interpolation variable, which greatly improves the computational efficiency. The problems of grid distortion make up the obvious defects of the finite element method in dealing with large deformation, nonlinear mechanics and other problems. It has high practical value and wide application prospect. The results of the program calculation are compared with the analytical solution and the finite element calculation results, which verify the correctness and rationality of the program.
2, based on the variational principle, the P- delta effect of a super long pile under the joint action of transverse and longitudinal loads is calculated and the element stiffness correction matrix is derived. In view of the large deformation of a super long pile under the joint action of transverse and longitudinal loads, a meshless natural element method for calculating the nonlinear large deformation is established. The P- delta effect shows that the displacement response of the pile is nonlinear due to the P- delta effect. The effect of the P- delta effect on the displacement and internal force of the pile can not be ignored when the soil quality is poor and the free length of the pile is large. This method provides a simple and easy method to consider the P- delta effect in the calculation. It has a certain value in engineering design and construction.
3, based on the meshless natural element method, the effects of load size, loading order, length diameter ratio, pile top constraint conditions, horizontal load position, relative stiffness ratio of pile and soil and load distribution form on the horizontal bearing capacity of super long pile are analyzed and the related conclusions are obtained.
4, when the p-y curve method is used to simulate the nonlinear characteristics of pile soil, the calculation error of the horizontal displacement of pile soil increases with the increase of load. In this paper, the longitudinal continuity of soil is considered by the theory of layered elastic system, and the layered soil is used to establish the layered soil foundation. The horizontal displacement coefficient transfer matrix method is used. According to the calculation principle of the equivalent load of the finite element, the horizontal displacement coefficient matrix is derived, and the modified formula of the horizontal displacement of the soil around the pile under the p-y curve is given when the external load is large. According to the established program, the horizontal displacement coefficient matrix of a three layer ground soil is calculated and divided. The correctness and rationality of the method is verified. As the longitudinal continuity of the soil is taken into account, the curve of the influence coefficient of horizontal displacement obtained by this method is more smooth than the Mindlin solution in the loading point and its adjacent area, and the displacement is less than the result of Mindlin solution. It can better reflect the difference between the actual distribution of layered soil and the interaction between adjacent soil layers.
【学位授予单位】：上海大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：TU473.1
本文编号：2169917
[Abstract]:With the development of science, the application of numerical methods to engineering is becoming more and more extensive, and the finite element method is the most widely used in engineering. However, the finite element method has the defects of grid distortion or entanglement in the nonlinear mechanical problems dealing with large deformation. At the same time, the finite element method is used to solve the liquid vibration, crack propagation, material transformation and forming. In the case of boundary or movable boundary, it is necessary to remesh the grid, and the physical quantity conversion between the old and the old grids will produce new errors. Therefore, the meshless method emerges as the times require. The unit method has gained rapid development with its unique advantages.
At present, super long piles are widely used in super high rise buildings, large span bridges and deepwater port engineering. However, the research of super long piles is relatively lagging at the present stage. In the project, the design is still in accordance with the common pile theory. The existing theory and analysis model can not fully consider the effects of the characteristics of layered soil or vertical and longitudinal loads. Bearing behavior of long piles, especially in port engineering, super long piles usually bear large horizontal loads, and large deformation often occurs under the joint action of transverse and longitudinal loads, and the traditional finite element method has the problems of lattice distortion or entanglement in the interaction of large deformation super long piles and soil.
In this paper, the interpolation function is further improved on the basis of the theory of natural element method, and applied to the horizontal bearing capacity of the super long pile in the layered foundation. The main research work and innovation points are as follows:
1, the interpolation function of the natural element method is improved and the three-dimensional meshless natural element method is developed. This paper uses the edge elements of the two order structure in the Voronoi diagram as the interpolation variable, which greatly improves the computational efficiency. The problems of grid distortion make up the obvious defects of the finite element method in dealing with large deformation, nonlinear mechanics and other problems. It has high practical value and wide application prospect. The results of the program calculation are compared with the analytical solution and the finite element calculation results, which verify the correctness and rationality of the program.
2, based on the variational principle, the P- delta effect of a super long pile under the joint action of transverse and longitudinal loads is calculated and the element stiffness correction matrix is derived. In view of the large deformation of a super long pile under the joint action of transverse and longitudinal loads, a meshless natural element method for calculating the nonlinear large deformation is established. The P- delta effect shows that the displacement response of the pile is nonlinear due to the P- delta effect. The effect of the P- delta effect on the displacement and internal force of the pile can not be ignored when the soil quality is poor and the free length of the pile is large. This method provides a simple and easy method to consider the P- delta effect in the calculation. It has a certain value in engineering design and construction.
3, based on the meshless natural element method, the effects of load size, loading order, length diameter ratio, pile top constraint conditions, horizontal load position, relative stiffness ratio of pile and soil and load distribution form on the horizontal bearing capacity of super long pile are analyzed and the related conclusions are obtained.
4, when the p-y curve method is used to simulate the nonlinear characteristics of pile soil, the calculation error of the horizontal displacement of pile soil increases with the increase of load. In this paper, the longitudinal continuity of soil is considered by the theory of layered elastic system, and the layered soil is used to establish the layered soil foundation. The horizontal displacement coefficient transfer matrix method is used. According to the calculation principle of the equivalent load of the finite element, the horizontal displacement coefficient matrix is derived, and the modified formula of the horizontal displacement of the soil around the pile under the p-y curve is given when the external load is large. According to the established program, the horizontal displacement coefficient matrix of a three layer ground soil is calculated and divided. The correctness and rationality of the method is verified. As the longitudinal continuity of the soil is taken into account, the curve of the influence coefficient of horizontal displacement obtained by this method is more smooth than the Mindlin solution in the loading point and its adjacent area, and the displacement is less than the result of Mindlin solution. It can better reflect the difference between the actual distribution of layered soil and the interaction between adjacent soil layers.
【学位授予单位】：上海大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：TU473.1
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