Vol. 5, No. 5, 2010

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ISSN: 1559-3959
Application of the Kirchhoff hypothesis to bending thin plates with different moduli in tension and compression

Xiao-ting He, Qiang Chen, Jun-yi Sun, Zhou-lian Zheng and Shan-lin Chen

Vol. 5 (2010), No. 5, 755–769
Abstract

When materials that exhibit different mechanical behaviors in tension and compression must be analyzed, Ambartsumyan’s bimodular model for isotropic materials can be adopted. It deals with the principal stress state in a point, which is particularly important in the analysis and design of reinforced concrete structures. However, due to the inherent complexity of the constitutive relation, it is difficult to solve analytically for bending components with bimoduli except in particular simple problems. Here we propose a simplified mechanical model, based on the classical Kirchhoff hypothesis, used for the solution of the bimodular thin plates in bending. We first use the Kirchhoff hypothesis to judge the existence of the elastic neutral layers of bimodular thin plates in small-deflection bending. Based on the existent neutral layers, we extend the solution from the case of pure bending into the case of lateral force bending. We use the displacement variation method to illustrate the application of the proposed model, and compare it with FEM results strictly based on Ambartsumyan’s materials model. The comparisons show that the proposed mechanical model is valid and helpful for analyzing bending structures with bimodularity.

Keywords
bimodulus, tension and compression, Kirchhoff hypothesis, plates, neutral layer
Milestones
Received: 4 October 2009
Revised: 2 February 2010
Accepted: 2 February 2010
Published: 3 December 2010
Authors
Xiao-ting He
College of Civil Engineering
Chongqing University
Chongqing 400045
China
Key Laboratory of New Technology for Construction of Cities in Mountain Area
Chongqing University
Ministry of Education
Chongqing 400045
China
Qiang Chen
College of Civil Engineering
Chongqing University
Chongqing 400045, China
Jun-yi Sun
College of Civil Engineering
Chongqing University
Chongqing 400045
China
Zhou-lian Zheng
College of Civil Engineering
Chongqing University
Chongqing 400045
China
Shan-lin Chen
College of Civil Engineering
Chongqing University
Chongqing 400045
China