On the Generalized Plane Stress Problem, the Gregory Decomposition and the Filon Mean Method
Source abstract
Abstract
In the present paper a stress general solution is obtained for the generalized plane stress problem with planar body forces, and it is demonstrated that only body force of biharmonic type ensures the compatibility with the generalized plane stress assumptions (σ 33=0). Inspired by the Filon perspective of average values, two more generalized plane stress problems with weak assumptions on the out-of-plane stress averages ((ar{sigma}33=0) or ( abla2 ar{sigma}33=0)) are studied, and the averages of the corresponding stress fields are expressed by the Airy stress functions. The authors also provide an alternative proof of the Gregory decomposition theory.
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Research context
OpenAlex topics: Composite Structure Analysis and Optimization · Elasticity and Material Modeling · Numerical methods in engineering
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References (17)
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