一対の内湾曲線で薄肉・厚肉に領域分割された部分円筒シェルの構造的特徴

Abstract

In early days as in the 1940s, a partial cylindrical concrete shell (long shell) was frequently used as a barrel roof structure. Many detailed investigations have been carried out, since the advent of ASCE Manuals of Engineering Practice in 1952. As a result, it has been found difficult to realize a strict membrane stress field in the barrel-roof-type shell, because the number of stress unknowns is unfit for the number of available boundary conditions. In a previous paper, the present author showed that a shell segment cut out from a circular cylinder with particular shapes and boundaries was able to satisfy the condition of membrane stress field. In this paper, a segment of partial circular cylinder is investigated, which is partitioned into three parts, by a pair of concave curves into the central thick shell zone with both fixed boundaries parallel to the generator, and two outer thin shell zones. The left half of the circular shell segment under consideration is taken to be the mirror image of the right half, or vice versa. Each of the left and right thin shell zones has shapes and boundaries that satisfy the requirement of a membrane stress state, in a way similar to the case in the previous paper. The central thick shell zone, on the other hand, behaves like an arch in which breadth and depth vary in the circular direction, keeping a constant cross-sectional area. It is noted that similarity exists with regard to the differential equations which relate displacement (denoted as V) in the circular direction with the displacements in the normal direction (denoted as W), between each circular cylinder in membrane stress states and the circular arch with a varied cross-section. This fact assures continuity of displacements along the concave partition lines. Thus, given a method of distributing suitable thickness to each shell zone, the outer thin shell zones in membrane stress states are cantilever-supported by the inner thick shell zone treated as an arch with varying cross-section along the circular direction. After solving the outer thin shell zones by a membrane theory presented in the previous paper, and after introducing pertinent parameters to describe the adequate shell-thicknesses with related shell shape, the thick shell zone is analyzed by solving a set of differential equations on the basis of the arch theory led by eliminating the longitudinal distribution in the general shell theory on a circular cylinder (the Flügge's Theory), including these parameters. The results of these parametric analyses are herein presented, and it is confirmed that the partial circular cylinder partitioned into a thick shell and two thin shells by a pair of concave curves can be solved as the Membrane Shell-Arch structure theoretically. For comparison, a typical example is selected with consideration of the results of above parametric analyses, and is analyzed by the Finite Element Method of Weak Form, equivalent to the Galerkin Method, by minimizing directly the total potential energy of a general circular cylindrical shell in which finite elements are able to express not only membrane deformations, but also bending deformations. This comparison with the FEM results indicates the adequacy of the proposed Membrane Shell-Arch Theory. From another point of view, the method introduced here serves as a means of determining an economical thickness distribution, in the design of a shell roof to cover a large space.