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The method of the finite elements is an adaptable numerical procedure for interpolation as well as for the numerical approximation of solutions of partial differential equations. The basis of these procedure is the formulation of suitable finite elements and element decompositions of the solution space. Classical finite elements are based on triangles or quadrangles in the two-dimensional space and tetrahedron or hexahedron in the threedimensional space. The use of arbitrary-dimensional convex and non-convex polyhedrons as the geometrical basis of finite elements increases the flexibility of generating finite element decompositions substantially and is sometimes the only way to get a clear decomposition...
We propose an enhanced iterative scheme for the precise reconstruction of piezoelectric material parameters from electric impedance and mechanical displacement measurements. It is based on finite-element simulations of the full three-dimensional piezoelectric equations, combined with an inexact Newton or nonlinear Landweber iterative inversion scheme. We apply our method to two piezoelectric materials and test its performance. For the first material, the manufacturer provides a full data set; for the second one, no material data set is available. For both cases, our inverse scheme, using electric impedance measurements as input data, performs well.
In this paper, systematic analyses for the shoring systems installed to support the applied loads during construction are performed on the basis of the numerical approach. On the basis of a rigorous time-dependent analysis, structural behaviors of reinforced concrete (RC) frame structures according to the changes in design variables such as the types of shoring systems, shore stiffness and shore spacing are analyzed and discussed. The time-dependent deformations of concrete such as creep and shrinkage and construction sequences of frame structures are also taken into account to minimize the structural instability and to reach to an improved design of shoring system because these effects may increase the axial forces delivered to the shores. In advance, the influence of the column shortening effect, generally mentioned in a tall building structure, is analyzed. From many parametric studies, it has been finally concluded that the most effective shoring system in RC frame structures is 2S1R (two shores and one reshore) regardless of the changes in design variables.
Development and Analysis of Sparse Matrix Concepts for Finite Element Approximation on general Cells
(2004)
In engineering and computing, the finite element approximation is one of the most well-known computational solution techniques. It is a great tool to find solutions for mechanic, fluid mechanic and ecological problems. Whoever works with the finite element method will need to solve a large system of linear equations. There are different ways to find a solution. One way is to use a matrix decomposition technique such as LU or QR. The other possibility is to use an iterative solution algorithm like Conjugate Gradients, Gauß-Seidel, Multigrid Methods, etc. This paper will focus on iterative solvers and the needed storage techniques...
For modeling of singular fields of stresses and deformations in elasters with a crack is offered to use of three-dimesional a special finite element. Weak compessible of elasters is taken into account on the basis of threefold approximation of fields of displacements, deformations and function of volume change. At intensive cyclic loading of the elastomer constructions with a crack it is necessary to take into account warming and large deformations at the crack top. The stress-deformed state elasters with a crack is determined from the decision of a nonlinear problem by a modified method Newton-Kantorovich. Account stress intensity factors for a rectangular plate with a various arrangement of a through crack is executed. Process of development of a surface crack and dissipative warming in prismatic a element of shift is investigated.
The paper investigates accuracy of deflection predictions made by the finite element package ATENA and design code methods ACI and EC2. Deflections have been calculated for a large number of experimental reinforced concrete beams reported by three investigators. Statistical parameters have been established for each of the technique at different load levels, separately for the beams with small and moderate reinforcement ratio.
In this paper we present a theoretical background for a coupled analytical–numerical approach to model a crack propagation process in two-dimensional bounded domains. The goal of the coupled analytical–numerical approach is to obtain the correct solution behaviour near the crack tip by help of the analytical solution constructed by using tools of complex function theory and couple it continuously with the finite element solution in the region far from the singularity. In this way, crack propagation could be modelled without using remeshing. Possible directions of crack growth can be calculated through the minimization of the total energy composed of the potential energy and the dissipated energy based on the energy release rate. Within this setting, an analytical solution of a mixed boundary value problem based on complex analysis and conformal mapping techniques is presented in a circular region containing an arbitrary crack path. More precisely, the linear elastic problem is transformed into a Riemann–Hilbert problem in the unit disk for holomorphic functions. Utilising advantages of the analytical solution in the region near the crack tip, the total energy could be evaluated within short computation times for various crack kink angles and lengths leading to a potentially efficient way of computing the minimization procedure. To this end, the paper presents a general strategy of the new coupled approach for crack propagation modelling. Additionally, we also discuss obstacles in the way of practical realisation of this strategy.
This study is focused on finite element analysis of a model comprising femur into which a femoral component of a total hip replacement was implanted. The considered prosthesis is fabricated from a functionally graded material (FGM) comprising a layer of a titanium alloy bonded to a layer of hydroxyapatite. The elastic modulus of the FGM was adjusted in the radial, longitudinal, and longitudinal-radial directions by altering the volume fraction gradient exponent. Four cases were studied, involving two different methods of anchoring the prosthesis to the spongy bone and two cases of applied loading. The results revealed that the FG prostheses provoked more SED to the bone. The FG prostheses carried less stress, while more stress was induced to the bone and cement. Meanwhile, less shear interface stress was stimulated to the prosthesis-bone interface in the noncemented FG prostheses. The cement-bone interface carried more stress compared to the prosthesis-cement interface. Stair climbing induced more harmful effects to the implanted femur components compared to the normal walking by causing more stress. Therefore, stress shielding, developed stresses, and interface stresses in the THR components could be adjusted through the controlling stiffness of the FG prosthesis by managing volume fraction gradient exponent.
When it comes to monitoring of huge structures, main issues are limited time, high costs and how to deal with the big amount of data. In order to reduce and manage them, respectively, methods from the field of optimal design of experiments are useful and supportive. Having optimal experimental designs at hand before conducting any measurements is leading to a highly informative measurement concept, where the sensor positions are optimized according to minimal errors in the structures’ models. For the reduction of computational time a combined approach using Fisher Information Matrix and mean-squared error in a two-step procedure is proposed under the consideration of different error types. The error descriptions contain random/aleatoric and systematic/epistemic portions. Applying this combined approach on a finite element model using artificial acceleration time measurement data with artificially added errors leads to the optimized sensor positions. These findings are compared to results from laboratory experiments on the modeled structure, which is a tower-like structure represented by a hollow pipe as the cantilever beam. Conclusively, the combined approach is leading to a sound experimental design that leads to a good estimate of the structure’s behavior and model parameters without the need of preliminary measurements for model updating.
Creation of hierarchical sequence of the plastic and viscoplastic models according to different levels of structure approximations is considered. Developed strategy of multimodel analysis, which consists of creation of the inelastic models library, determination of selection criteria system and caring out of multivariant sequential clarifying computations, is described. Application of the multimodel approach in numerical computations has demonstrated possibility of reliable prediction of stress-strain response under wide variety of combined nonproportional loading.