| The availability of units in Semester 1, 2, full year, etc. was correct at the time of going to press but may be subject to change. For the most up-to-date information click on the Timetable link below. |
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| Credit: 6 points Availability: Semester 2 (See Timetable) |
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| Outcomes: By the end of this unit students understand the basic concepts in the theory of elasticity and gain the necessary skills for calculation of stresses, strains and displacements of elastic systems. This provides the foundations for understanding the mechanical behaviour and failure of engineering and geological structures. |
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Content: Topics include displacements and strains; compatibility conditions; stresses; equilibrium equations; principal stresses; hydrostatic and deviatoric parts; Mohr diagrams; elasticity; Hooke's law; isotropy and anisotropy; technical moduli (Young's modulus, Poison's ratio, bulk and shear moduli); general formulation of elastic problems; 2-D problems of elasticity; plane strain and plain stress conditions; anti-plane deformation; axially symmetric problem; formulation of boundary value problems in terms of displacements and stresses.
2-D problems include the virtual work principle; the Airy's function; simple solutions for the beam; comparison with the beam theory; Saint-Venant principle; equations in polar co-ordinates; stress concentration near holes; elementary solutions for the plane with a circular hole; plane problems; Fourier transform; solutions for semi-plane and beam; plane problems; Mellin transform; solution for wedge-like domains; homogeneous solutions.
Fundamental solutions include concentrated force and dislocations; mass forces and temperature effects; modification of elastic equations; simple thermo-elastic problems; introduction to the general theory of the plane elastic problems; complex variables; functions of complex variables; single and multi-valued functions; holomorphic functions; integration of complex-valued functions; Integral Cauchy's theorem; Integral Cauchy's formula; the Sokotskij-Plemelj formulae; plane elastic problems; transformation of general equations; general solution by means of complex potentials; Kolosov-Muskhelishvili formulae; analytical solutions of plane elastic problems for simple domains. |
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| Assessment: This consists of examination worth 50 per cent, three assignments worth 25 per cent and a project worth 25 per cent. The examination is in an open-book format. The purpose is to test the student’s ability to solve problems. Assessment of assignments is based on written reports which must be clear, concise and informative. Projects require literature search and numerical calculations with the use of available computer programs to solve engineering problems, and hence, they test the student’s ability to formulate and solve problems. |
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| Unit Co-ordinator(s): Dr Alexander Galybin |
| Location: UWA (Crawley) |
| Mode: on-campus |
Unit Rules: |
| Advisable prior study: Statics and Solid Mechanics 213 (610.213) |
Contact hours—65 (lectures:39 hrs; tutorials:26 hrs)
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Unit Web Page: http://www.civil.uwa.edu.au/ |
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Recommended Reading
England, A. H. Complex Variable Methods in Elasticity: John Wiley & Sons 1971
Muskhelishvili, N. I. Some Basic Problems of the Mathematical Theory of Elasticity: P. Noordhoff 1953
Timoshenko, S. P. and Goodier, J. N. Theory of Elasticity: McGraw-Hill 1969
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Books and other material wherever listed may be subject to change.
Book lists relating to 'Preliminary Reading', 'Recommended Reading' and 'Textbooks' are, in most cases, available at the University Co-operative Bookshop (from early January) and appropriate administrative offices for students to consult. For first-year units the Bookshop will endeavour to make available photocopies of book lists for individual units. Books marked with an asterisk (*) are available in paperback. |
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