FINITE ELEMENT METHOD ACCURACY FOR WAVE PROPAGATION PROBLEMS

THE RESULTS ARE PRESENTED OF A STUDY CONCERNING THE ACCURACY OF DISPLACEMENTS CAUSED BY A SINGLE, HARMONIC, ONE-DIMENSIONAL ELASTIC WAVE PROPAGATING THROUGH A FINITE ELEMENT MESH. A FINITE MODEL OF THE SEMI-INFINITE CONSTRAINED ROD THAT WAS DEVELOPED IS ILLUSTRATED. THE DASHPOT CONSTANT REQUIRED IN DESIGNING THE FINITE MODEL (ILLUSTRATED) SUCH THAT PERFECT ABSORPTION OF THE NORMALLY INCIDENT ELASTIC WAVE IS ATTAINED, CAN BE DETERMINED FROM ONE DIMENSIONAL WAVE PROPAGATION THEORY. A FINITE ELEMENT ANALYSIS WAS PERFORMED FOR BOTH THE PLANE STRAIN AND THE AXISYMMETRIC PROBLEMS USING RECTANGULAR ELEMENTS. SOLUTIONS FOR BOTH THE PLANE STRAIN CASE AND THE AXISYMMETRIC CASE WERE OBTAINED; THE RESULTS FOR BOTH CASES WERE IDENTICAL WHEN USING THE CONSISTENT MASS MATRIX, BUT DIFFERED BY AN INSIGNIFICANT AMOUNT WHEN THE MASS WAS LUMPED AT NODAL POINTS. ONLY THE PLANE STRAIN RESULTS ARE PRESENTED. A DISCUSSION OF ERROR ANALYSIS GIVES CONSIDERATION TO THE HOMOGENEOUS ROD AND THE TWO-MATERIAL ROD. THE CONSTRAINED ROD IS THE SIMPLEST OF ALL PROBLEMS INVOLVING ELASTIC WAVES PROPAGATING IN SEMI-INFINITE SYSTEMS BECAUSE ONLY ONE WAVE TYPE EXISTS AND ITS DIRECTION IS KNOWN. THEREFORE, THE STRESS DUE TO THE PROPAGATING PLANE WAVE IS KNOWN AND MAY BE APPLIED TO THE BASE OF THE FINITE ROD. REPRESENTING THE FINITE ROD BY A SYSTEM OF FINITE ELEMENTS PERMITS A RIGOROUS ANALYSIS OF THE ACCURACY OF THE FINITE ELEMENT METHOD FOR APPROXIMATING THE ELASTIC CONTINUUM IN STEADY STATE WAVE PROPAGATION PROBLEMS. THE RESULTS FOR THE STEADY-STATE RESPONSE OF A FINITE MODEL OF SEMI-INFINITE ELASTIC CONSTRAINED ROD ARE DISCUSSED. THE USE OF THE CONSISTENT MASS MATRIX IS DISCUSSED. THE ADVANTAGES IN THE USE OF THE LUMPED MASS MATRIX TO SOLVE TRANSIENT PROBLEMS IS CONSIDERED TO BE THE COMPUTER STORAGE SPACE SAVING. USE OF THE COMPLEX VECTOR METHOD TO SOLVE STEADY STATE DYNAMICS PROBLEMS, REPRESENTS NO SUCH SAVING.

• Supplemental Notes:
  • 2 APP
• Authors:
  • Kuhlemeyer, R L
  • LYSMER, J
• Publication Date: 1973-5

Media Info

• Features: Figures; References;
• Pagination: p. 421-7
• Serial:
  • Journal of Soil Mechanics & Foundations Div
  • Volume: 99
  • Issue Number: sm5

Subject/Index Terms

• TRT Terms: Accuracy; Analysis; Dislocation (Geology); Errors; Finite element method; Harmonics; Mathematical models; Methodology; Problem solving; Wave motion
• Uncontrolled Terms: Models
• Old TRIS Terms: Axisymmetric systems; Elastics; Finite elements
• Subject Areas: Geotechnology; Highways;

Filing Info

• Accession Number: 00236673
• Record Type: Publication
• Report/Paper Numbers: Tech Rpt
• Files: TRIS
• Created Date: May 15 1974 12:00AM