ABSTRACT
Shells are thin, curved structures such as pressure vessels, pipes, domes, caps, etc. While plates and beams resist transverse loads through bending, shells react to transverse loads mainly through membrane forces N x $ N_{x} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315296494/ddaf5c6c-59eb-45c6-9191-bbd0c8a81172/content/inline-math12_1.tif"/> , N y $ N_{y} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315296494/ddaf5c6c-59eb-45c6-9191-bbd0c8a81172/content/inline-math12_2.tif"/> , N x y $ N_{xy} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315296494/ddaf5c6c-59eb-45c6-9191-bbd0c8a81172/content/inline-math12_3.tif"/> . Bending moments M x $ M_{x} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315296494/ddaf5c6c-59eb-45c6-9191-bbd0c8a81172/content/inline-math12_4.tif"/> , M y $ M_{y} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315296494/ddaf5c6c-59eb-45c6-9191-bbd0c8a81172/content/inline-math12_5.tif"/> , M x y $ M_{xy} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315296494/ddaf5c6c-59eb-45c6-9191-bbd0c8a81172/content/inline-math12_6.tif"/> are usually quite small over most of the shell except around the points of application of concentrated loads and around the supports. Knowledge of the membrane forces is sufficient in most cases for preliminary design of shells, and often no other computations are required. If precise information about stresses near support or load points is required, a finite element analysis can be done at a later stage in the design process. However, the major decisions about materials, fiber architecture, and geometry are likely to be done at an early stage using membrane analysis.
