The resultant linear six‐field theory of elastic shells: What it brings to the classical linear shell models?

Abstract

Basic relations of the resultant linear six‐field theory of shells are established by consistent linearization of the resultant 2D non‐linear theory of shells. As compared with the classical linear shell models of Kirchhoff‐Love and Timoshenko‐Reissner type, the six‐field linear shell model contains the drilling rotation as an independent kinematic variable as well as two surface drilling couples with two work‐conjugate surface drilling bending measures are present in description of the shell stress‐strain state. Among new results obtained here within the six‐field linear theory of elastic shells there are: 1) formulation of the extended static‐geometric analogy; 2) derivation of complex BVP for complex independent variables; 3) description of deformation of the shell boundary element; 4) the Cesáro type formulas and expressions for the vectors of stress functions along the shell boundary contour; 5) discussion on explicit appearance of gradients of 2D stress and strain measures in the resultant stress working.