A Class of Stability Problems: Sequential Fabrication of Expandable Structures

Abstract

Sequential fabrication of expandable structures has been investigated as a class of stability problems. When a system is fabricated in a multistage process, the erection procedure generates a set of geometric and stress boundary conditions which enter the governing equations for the resulting system. The system evolves through a series of unstable configurations until it reaches a final stable state. A systematic approach is presented to model the stress path in the system being fabricated. The proposed algorithm has been discussed for prestressed elastica arches and pre-buckled sandwich arches. A nonlinear finite element method using crotational formulation of a two-node, three-layer sandwich beam element has been developed to model the fabrication process of the arch. The model is then used to predict the buckling and post-buckling behaviour of the sandwich arch.

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References

Tang

M.C.

, Lenticular Air Inflated Bubble Roof Structures, Proceedings of the ASCE Symposium on Long Span Roof Structures, New York, 1981.

Escrig

, Expandable Space Structures, International Journal of Space Structures, 1(2), 1985, 79–91.

Foster

C.G.

and Krishnakumar

, A Class of Transportable Demountable Structures, International Journal of Space Structures, 2(3), 1986, 129–137.

Meyers

V.J.

, Pneumatically Formed Sandwich Shell Roof, Journal of Structural Division, ASCE, 104(3), 1978, 381–389

Hanghai

., Shape Finding Analysis of Air-Supported Membrane Structures in the Process of Inflation, Proceedings of the International Symposium on Innovative Applications of Shells and Spatial Forms, 1988, 657–666.

Mallett

R.H.

, Stresses Due to Assembly of Parts, in: Dietrich

D.E.

, ed, 1991 ANSYS Conference Proceedings (Vol. 1), Swanson Analysis Systems, 1991, 50–62.

Clifton

R.J.

, Snap-Buckling of Shallow Prestressed Arches, Journal of Engineering Mechanics, ASCE, 96(6), 1970, 1157–1170.

Thompson

J.M.T.

and Hunt

G.W.

, On the Buckling and Imperfection-Sensitivity of Arches With and Without Prestress, International Journal of Solids and Structures, 10(5), 1983, 445–459.

Chini

S.A.

and Wolde-Tinsae

A.M.

, Critical Load and Postbuckling of Arch Frameworks, Journal of Engineering Mechanics, ASCE, 114(9), 1988, 1435–1453.

10.

Huddleston

J.V.

, Behaviour of a Steep Prestressed Arch made from a Buckled Strut, Journal of Applied Mechanics. ASME, 37(4), 1970, 984–994.

11.

Wolde-Tinsae

A.M.

, Prebuckled Sandwich Domes and Super Domes, in: Heki

, ed, Shells, Membrane and Space Frames (Vol. 1): Proceedings of the IASS Symposium on Membrane Structures and Space Frames, Elsevier Science Publishers, Amsterdam, 1986, 345–352.

12.

Mirmiran

and Wolde-Tinsae

A.M.

, Expandable, Rapidly Assembled Sandwich Domes, Proceedings of the International Conference on Mobile and Rapidly Assembled Structures, Southampton, UK, 1991.

13.

Mirmiran

and Wolde-Tinsae

A.M.

, Nonlinear Finite Element Modeling for Erection of Prestressed Sandwich Arches, in: Sousa

, Brebbia

C.A.

and Carlomagno

G.M.

, ed, Proceedings of the 5th Conference on Computational Methods and Experimental Measurements, Elsevier Science Publishers, New York, 1991, 543–554.

14.

Mirmiran

, Nonlinear Stability Analysis of Prestressed Sandwich Arches Using the Finite Elemem Method, Ph.D. Thesis, University of Maryland at College Park, MD., 1991.