Abstract
Direct modeling and simulation of engineering problems with various irregularities are computationally very inefficient and in some cases impossible, even in these days of massively parallel computational systems. As a result, in recent times, a number of schemes have been put forward to tract such problems in a computationally efficient manner. Needless to say, such schemes are still going through evolutionary stages. This paper addresses direct solution based on the selective use of different dimensional models at different regions of the problem domain. For the multidimensional approach, a higher-order transition element is developed to connect the different element types where two- and three-dimensional laminated elements based on higher-order subparametric concept are considered. Modeling simplicity and calculation efficiency of the multidimensional approach are shown for the analysis of cantilever plates with stepped section and patch-repaired plates.
Highlights
A finite element method is one of versatile numerical tools to solve some differential equations which model physical phenomena of various engineering problems
Lower-order finite elements have been conventionally used to solve a wide range of practical problems
Even though one uses a highly refined mesh to model problems having significant stress gradients, the accuracy of stresses obtained by using lower-order finite elements is rather poor [1]
Summary
A finite element method is one of versatile numerical tools to solve some differential equations which model physical phenomena of various engineering problems. The most popular approach for connecting different mathematical models (like simultaneous twodimensional to three-dimensional modeling of plates and shells) is to implement special transition elements [20,21,22,23] Those researches adopt finite element mesh using conventional lower-order functions. The performance of those finite elements has not been satisfactory in predicting smooth and accurate variations of stresses as well as displacements for plates with various irregularities. When the structures are modeled by function refined mesh technique to reduce negative effect from various irregularities, this multidimensional analysis proposed in this work can be considered This proposed method can be attempted to distribute limited computational resources in an optimal manner to achieve maximum solution accuracy with minimal solution cost, subject to certain problem-specific constraints
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