Bending of rectangular orthotropic plates with rotationally restrained and free edges: Generalized integral transform solutions

2021 ◽  
Vol 247 ◽  
pp. 113129
Author(s):  
Yangye He ◽  
Menglan Duan ◽  
Jian Su
Keyword(s):  
Integral Transform ◽  
Orthotropic Plates ◽  
Free Edges

ANALYTICAL AND FINITE ELEMENT MODELING AND SIMULATION OF BUCKLING AND POSTBUCKLING OF DELAMINATED ORTHOTROPIC PLATES

2011 ◽  
Vol 02 (01) ◽  
pp. 97-104 ◽  
Author(s):  
LALITHA CHATTOPADHYAY ◽  
S. SRIDHARA MURTHY
Keyword(s):  
Finite Element ◽  
Strain Energy ◽  
Failure Modes ◽  
Integral Transform ◽  
Laminated Composite ◽  
Strain Energy Release ◽  
Orthotropic Plates ◽  
Manufacturing Defects ◽  
Laminated Composite Materials ◽  
Plane Compression

Delamination is one of the most common failure modes of laminated composite materials, and can be caused by manufacturing defects or impact loading. Under compression, a delaminated composite plate may buckle and tend to enlarge the delaminated area, which can lead to loss of global structural stability. This paper presents the elastic buckling and postbuckling analysis of an axially loaded beam-plate with an across-the-width delamination, located at a given depth below the upper surface of the plate. The analysis is done by considering a layered orthotropic plate containing through-width delamination, subjected to in-plane compression. The problem is analyzed by two approaches: (i) A simple analytical model for determining strain energy release rate is obtained using integral transform approach; (ii) A finite element representation of the problem is modeled and analyzed using MSC/NASTRAN and the buckling load is calculated.

New Straightforward Benchmark Solutions for Bending and Free Vibration of Clamped Anisotropic Rectangular Thin Plates

2021 ◽  
pp. 1-24
Author(s):  
Dongqi An ◽  
Zhuofan Ni ◽  
Dian Xu ◽  
Rui Li
Keyword(s):  
Free Vibration ◽  
Numerical Solutions ◽  
Integral Transform ◽  
Integral Transforms ◽  
Thin Plates ◽  
Orthotropic Plates ◽  
Transform Method ◽  
Finite Integral ◽  
Benchmark Solutions ◽  
Similar Complex

Abstract This study presents new straightforward benchmark solutions for bending and free vibration of clamped anisotropic rectangular thin plates by a double finite integral transform method. Being different from the previous studies that took pure trigonometric functions as the integral kernels, the exponential functions are adopted, and the unknowns to be determined are constituted after the integral transform, which overcomes the difficulty in solving the governing higher-order partial differential equations with odd derivatives with respect to both the in-plane coordinate variables, thus goes beyond the limit of conventional finite integral transforms that are only applicable to isotropic or orthotropic plates. The present study provides an easy-to-implement approach for similar complex problems, extending the scope of finite integral transforms with applications to plate problems. The validity of the method and accuracy of the new solutions that can serve as benchmarks are well confirmed by satisfactory comparison with the numerical solutions.

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