The Generation of Inter-Element-Compatible Stiffness and Mass Matrices by the Use of Interpolation Formulas
Report Number: AFFDL-TR-66-80 p. 395-443
Author(s): Bogner, F. K, Fox, R. L., Schmit, L. A., Jr.
Corporate Author(s): Case Institute of Technology
Laboratory: Air Force Flight Dynamics Laboratory
Date of Publication: 1966-11
Pages: 49
Contract: Laboratory Research - No Contract
DoD Task:
Identifier: This paper is part of a conference proceedings. See AD0646300
Abstract:
This paper presents a general method of subelement displacement states which makes it a relatively simple task to insure completely compatible displacement states. The method involves the use of Hermite interpolation formulas of various order. The total potential energy principle is used to generate stiffness matrices based on these displacement states. The approach is presented in general orthogonal curvilinear coordinates for shell type structures. Inter-element-compatible stiffness matrices are presented for a rectangular membrane, a rectangular plate with twelve degrees of freedom, and a rectangular plate with twenty four degrees of freedom. The corresponding consistent mass matrices are presented for both plate elements. Numerical examples of static deflection analysis are presented based on both of the plate subelements and the monotonic convergence of the discretization error is confirmed. Application of the simpler plate subelement to the determination of natural modes and frequencies is also illustrated with a numerical example. All of the examples are selected so that comparison with classical results can be made.
Provenance: Bombardier/Aero
Author(s): Bogner, F. K, Fox, R. L., Schmit, L. A., Jr.
Corporate Author(s): Case Institute of Technology
Laboratory: Air Force Flight Dynamics Laboratory
Date of Publication: 1966-11
Pages: 49
Contract: Laboratory Research - No Contract
DoD Task:
Identifier: This paper is part of a conference proceedings. See AD0646300
Abstract:
This paper presents a general method of subelement displacement states which makes it a relatively simple task to insure completely compatible displacement states. The method involves the use of Hermite interpolation formulas of various order. The total potential energy principle is used to generate stiffness matrices based on these displacement states. The approach is presented in general orthogonal curvilinear coordinates for shell type structures. Inter-element-compatible stiffness matrices are presented for a rectangular membrane, a rectangular plate with twelve degrees of freedom, and a rectangular plate with twenty four degrees of freedom. The corresponding consistent mass matrices are presented for both plate elements. Numerical examples of static deflection analysis are presented based on both of the plate subelements and the monotonic convergence of the discretization error is confirmed. Application of the simpler plate subelement to the determination of natural modes and frequencies is also illustrated with a numerical example. All of the examples are selected so that comparison with classical results can be made.
Provenance: Bombardier/Aero
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This report is part of the following conference:
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Matrix Methods in Structural Mechanics
AFFDL TR 66-80