Marko Matikainen Development of beam and plate finite elements based on the abs olute nodal coordinate formulation Lappeenranta, 2009 69 pages Acta Universitatis Lappeenrantaensis 359 Dissertation. Lappeenranta University of Technology ISBN 978-952-214-838-4 ISBN 978-952-214-839-1 (PDF) ISSN 1456-4491 The focus of this dissertation is to develop finite elements b ased on the absolute nodal coordinate formulation. The absolute nodal coordina te formulation is a nonlinear finite element formulation, which is introduced f or special requirements in the field of flexible multibody dynamics. In this form ulation, a special definition for the rotation of elements is employed to ensure the formulation will not suffer from singularities due to large rotations. The ab solute nodal coordinate formulation can be used for analyzing the dynamics of beam, p late and shell type structures. The improvements of the formulation are mainly concentrate d towards the description of transverse shear deformation. Additionally, the formulation is verified by using conventional iso-parametric solid finite eleme nt and geometrically exact beam theory. Previous claims about especially high ei enfrequencies are studied by introducing beam elements based on the absolute n odal coordinate formulation in the framework of the large rotation vector ap proach. Additionally, the same high eigenfrequency problem is studied by usi ng constraints for transverse deformation. It was determined that the improvements for shear deformati on in the transverse direction lead to clear improvements in computational effic i n y. This was especially true when comparative stress must be defined, for ex ample when using elasto-plastic material. Furthermore, the developed plat e element can be used to avoid certain numerical problems, such as shear and curva ture lockings. In addition, it was shown that when compared to conventional so lid elements, or elements based on nonlinear beam theory, elements based on t he absolute nodal coordinate formulation do not lead to an especially stiff sy stem for the equations of motion.

Theory of matrix structural analysis

Development of beam and plate finite elements based on the absolute nodal coordinate formulation

The objective of this paper is to develop a mechanical design method for doweled joint. In order to investigate the mechanical behavior of dowel bar, a mechanical model for dowel bar in transverse joint of concrete pavement based on the three dimensional finite element method PAVE3D was developed. In the model, a dowel bar is divided into two segments embedded in concrete and a segment between them and these segments are modeled by the solution of the beam on elastic foundation and the three dimensional beam element, respectively. The model was verified by comparing the predicted strains in concrete slab and dowel bar with the experimental data that were obtained from loading tests conducted on a model pavement and an actual pavement. The effects of transverse joint structure and subbase stiffness on the stresses in dowel bar and concrete slab were investigated based on numerical simulations with PAVE3D.

Study on mechanical behavior of dowel bar in transverse joint of concrete pavement

For stiffness design optimization of composite frame structures, one of the major problems when using fiber winding angles as design variables directly is the lack of convexity of the objective function, which may lead to different local optima depending on initial designs when a traditional gradient-based optimization algorithm is applied. Therefore, the present paper adopts a gradient-based two-step optimization scheme to cope with the difficulty and search for a better optimal design of composite frames in which the fiber winding angles are taken as design variables. To realize the two-step optimization scheme, the equivalent stiffness parameters of a composite beam with circular cross-section are derived in explicit expressions and used to force the convexity of the design optimization of the composite frame. The stiffness matrices are linearly expressed in terms of the stiffness parameters, which guarantee the convexity of the design variable feasible region in the stiffness parameter space. The equivalent stiffness parameters are adopted to keep invariance of physical quantities between fiber winding angle and equivalent stiffness parameter spaces. In the two-step optimization scheme, the minimum identification problem with the constraint that the objective function at the new starting point is less than or equal to the previous objective function at the optimum point in fiber winding angle space is established. Then, the two-step optimization scheme can be implemented in the fiber winding angle and structural equivalent stiffness parameter spaces, respectively, until the minimum identification problem is not possible to identify a new starting point. The proposed two-step optimization scheme for composite frames fully takes advantage of the stiffness parameters in convexity and fiber winding angles as practically physical quantities, respectively. The sensitivity information of the objective function with respect to fiber winding angles and equivalent stiffness parameters is derived by the analytical sensitivity analysis method. Numerical examples show that the two-step optimization scheme can effectively force convexity of the optimization model and help to eliminate the initial design dependency. The effectiveness of the proposed two-step scheme is further verified through the particle swarm optimization (PSO) algorithm which is an evolutionary algorithm with global optimization capability.

Theory of matrix structural analysis

Citations

Development of beam and plate finite elements based on the absolute nodal coordinate formulation

Study on mechanical behavior of dowel bar in transverse joint of concrete pavement

A two-step optimization scheme based on equivalent stiffness parameters for forcing convexity of fiber winding angle in composite frames

Comparing Soft-String and Stiff-String Methods Used to Compute Casing Centralization

Modeling and control of high speed machine tool feed drives

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