Static and dynamic analysis of cylindrical shell by different kinds of B-spline wavelet finite elements on the interval
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ORIGINAL ARTICLE
Static and dynamic analysis of cylindrical shell by different kinds of B‑spline wavelet finite elements on the interval Xingwu Zhang1,2 · Yanfei He1,2 · Zengguang Li3 · Zhi Zhai1,2 · Ruqiang Yan1,2 · Xuefeng Chen1,2 Received: 11 February 2019 / Accepted: 14 June 2019 © Springer-Verlag London Ltd., part of Springer Nature 2019
Abstract Cylindrical shell is a fundamental structure in the area of mechanical and architectural engineering. In the predesign stage, accurate analysis is a key step to guarantee the performance in application. Finite element method is a commonly used method in structural analysis. However, due to the limitations of interpolation functions, accuracy and efficiency are restricted. Wavelet finite element method is an advanced numerical method which uses wavelet functions to replace the traditional polynomial function to discrete the solving variables. Daubechies, B-spline wavelet on the interval (BSWI) etc. have been used to construct the elements. However, they are mainly focused on the elements with one kind of variable. That is, only the displacement variable is interpolated directly and the generalized stress and strain are calculated second. Multivariable wavelet finite element can deal with this problem, in which the three kinds of variables can be interpolated and solved directly, thus the calculation error can be avoiding. In this paper, the BSWI scaling functions are used to construct the wavelet finite elements for cylindrical shell, including BSWI element with one kind of variables (BSWI-WFE), BSWI element with two kinds of variables (BSWI-TwWFE) and BSWI element with three kinds of variables (BSWI-ThWFE). Several numerical examples for cylindrical shell are provided to analyze the performance of the constructed elements and compared with each other to indicate superiority and efficiency. Keywords Cylindrical shell · B-spline wavelet on the interval · Wavelet finite element method · Two kinds of variables · Three kinds of variables
1 Introduction Cylindrical shell is a commonly used structure in engineering applications, such as mechanical engineering and architectural engineering [1, 2]. Accurate static and dynamic analysis is the key procedure to guarantee the performance in actual applications. Finite element method (FEM) is a widely used method in structural analysis and achieved satisfying results in industrial numerical analysis. Such as, Tang et al. proposed a combined 3D discrete element and cylindrical shell FEM for simulating dynamic failure behavior * Zhi Zhai [email protected] 1
State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an 710049, Shaanxi, China
2
School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, Shaanxi, China
3
China Ship Development and Design Centre, Shanghai 201108, China
with inner pressure [3]. By introducing additional rotational DOF, Bourezane proposed an improved strain based cylindrical shell finite element and studied its performance [4]. Sheng e
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