Theory Of Non-Nodal Finite Element Methods And Its Realization In Software

In civil engineering, as the matrix material performance deficiencies, the reinforced materials are used largely to enhance and improve the mechanical properties of the structure. Ordinary reinforced concrete, pre-stressed reinforced concrete, and fiber reinforced concrete, steel reinforced concrete, concrete-filled steel tube, rock with a bolt anchoring, and other composite materials and forms of structural are widely used. Due to the structure's importance, the high accurate analysis is needed. To accurately analyze the reinforced structure with finite element method, the primary problem to be solved is to establish the appropriate finite element models. At present, the finite element models of the reinforced structure have three types: the discrete model, the embedded model and smeared model. However, for flaws in the three types, it is difficult to simulate the complicated reinforced structures in engineering.Lacking appropriate finite element analysis model of the reinforced structures in the civil engineering, the following aspects of the study are carried out and the corresponding results are obtained:1. Based on inspecting the mechanical behavior of reinforced components in the existing reinforced structure, that the reinforcement component can be meshed with truss elements and beam elements is indicated, and beam element has a wider scope of application as its integrated mechanical properties.2. On the basis of inspecting the various types of connectivity between reinforced components and the matrix material, the non-nodal connectivity method at the level of degrees of freedom is raised. Based on this method, the nodes of a reinforced element can be embedded into one or more other elements; while the node's DOF does not need to match the parent element's displacement field. This method is different from the discrete model in which the node-node connectivity is needed, and distinct from the embedded model in which the nodes of a reinforced element are all placed in the same parent element. Using the non-nodal connectivity method at the level of degrees of freedom, the reinforcement and its parent material can be meshed independently and expediently, furthermore the complex layout of reinforcements can be accurately considered. By introducing node coordinates, the displacement discontinuity between reinforced components and matrix materials, such as bond-slip, non-bonded, and disposed external, etc., can be simulated naturally. 3. In order to carry out the finite element analysis while the reinforcing element's nodes are embedded in one or more other elements, an in-depth study is conducted about the displacement field including rotational DOF in plane beam elements, space beam elements, plane isoparametric elements and space isoparametric elements. The rotational displacements are divided into two types of the point average rotation and the infinitesimal line's rotation, and their calculation formulas are given. The analysis of rotational displacements provides a theoretical basis to connect beam elements'nodes which have rotational DOFs with other elements, particularly when nodes are embedded in parent elements. Since nodes of a beam element can connect to their parent elements, the reinforcement can be meshed by beam elements successfully.4. The non-nodal connectivity finite element analysis method is established. An inner node's DOFs are divided into two types of dependence and independence. Under the coordinates at an inner node, the inner node's dependent DOFs are equal to the displacements accounted through its parent element, and the independent the others. A bond spring element between the inner node and its parent element is raised to simulate the bond-slip between the reinforcement and the matrix material. After the finite element formulas for multi types of elements are derived, the element assemble technique in the non-nodal connectivity state is worked out.5. The problem of bandwidth optimization in the non-nodal connectivity state is investigated. The bandwidth optimization technique can greatly improve the calculation speed of a FEM software, so is an indispensable function of a practical FEM software. Regarding the complicated circumstances of DOFs in the non-nodal connectivity state, some improvements in algorithm of graph theory are made to decrease the bandwidth; the bandwidth optimization algorithm is implemented at the level of DOF. This method resolves not only the complex issue of bandwidth optimization in the non-nodal connectivity state, but also the problem induced by that the DOFs numbers of various types of node taking part in the structure's whole DOFs are not equal.6. Using the object-oriented technology, a FEM software named RCF is developed to realize the non-nodal connectivity method, which provides a 3D graphical user interface and programmed in visual C++ language under the Windows platform. The levels of FEM classes are constructed in RCF. Making use of RCF and its 10 types of elements, the reinforced structures under plane and space circumstances can be meshed and analyzed by means of non-nodal connectivity method.7. A number of typical problems are calculated by RCF; their numerical results validate and demonstrate the correctness and feasibility of the software and the non-nodal connectivity finite element method.The non-nodal connectivity finite element method breaks the traditional restrictions of node-node connecting and adds new content to existing finite element theory. The flexible application of connecting technology and element types provides more choices to mesh a structure and afford new models at element level for a variety of reinforced structures in civil engineering, and can reveal more accurately the mechanical behavior of a structure at overall and its partial key parts, and therefore improve the finite element analysis for reinforced structures. The method has broad application prospects in civil engineering.