A NUMERICAL SOLUTION FOR THE TRANSIENT STRAIN DISTRIBUTION IN A RECTANGULAR PLATE WITH A PROPAGATING CRACK
A physical lattice model that approximates a continuous material by reducing it to a series of rigid bars and deformable connections is used in this report to investigate the transient-strain redistribution associated with a crack propagating through a rectangular plate. Equations are developed for equilibrium of the lattice model in terms of displacements using plane-stress conditions. A complete set of equations is given to cover all cases of boundary conditions that ordinarily would be encountered in applications of this lattice model. Results of several examples of statically loaded plates analyzed with the lattice model show excellent agreement when compared with an energy method solution. The differential equations expressing the dynamic behavior of the lattice model are developed, and numerical solution of these equations is discussed. Examples are given of application of these equations to a steady-state condition and the calculation of natural frequencies of lattice models. Several examples of the transient-strain redistribution associated with a crack propagating through a plate in finite jumps are presented. Two methods of numerical integration that are suitable for transient solutions of the differential equations are described and applied to the same problem with resulting comparable satisfactory solutions. An immense amount of calculation is involved in solving transient strain-wave propagation problems with the lattice model, and a high speed digital computer is virtually a necessity for numerical solution of problems of any complexity by this method.
University of Illinois, Urbana-ChampaignUrbana, IL United States 61801
Ship Structure CommitteeNational Academy of Science, 2101 Constitution Avenue, NW
Washington, DC United States 20418
- Gaus, M P
- Publication Date: 1961-9-5
- Features: References;
- Pagination: 78 p.
- TRT Terms: Cracking; Deformation curve; Finite element method; Fracture mechanics; Steel plates
- Identifier Terms: Ship Structure Committee
- Uncontrolled Terms: Crack propagation
- Subject Areas: Marine Transportation; Materials;
- Accession Number: 00331917
- Record Type: Publication
- Source Agency: Ship Structure Committee
- Report/Paper Numbers: SSC-129 Prog Rpt.
- Contract Numbers: NObs-65790, NObs-72046
- Files: TRIS
- Created Date: May 21 1981 12:00AM