Course syllabus for Solid mechanics

Solid Mechanics is a continuation of the course Statics and solid mechanics. We learn to construct and solve mathematical models. You need to have good background in the basic courses of Mathematics. More precisely knowledge about the following is needed:
Linear algebra:
vector algebra, matrix algebra, systems of linear equations,
eigenvalue problems

Calculus:
elementary functions (logarithmic, exponential, Hyperbolic, trigonometric).
inequalities, differential Calculus (derivatives, extremes of functions construction of curves), differential equations (separable, second and forth orders with constant coefficients, non-homogeneous, initial conditions). Solution of homogeneous equation and particular solution, Euler s differential equation, boundary value problems, basic theory on partial differential equations

Basic knowledge in Matlab (code structure, functions, matrix calculations, curve constructions, plotting).

The student should obtain the knowledge, skills and attitudes required for solving real world strength of materials problem by hand and by use of suitable numerical software (e.g., Matlab). The problems include design, analysis as well as prediction of function and reliability of constructions.

• Derive and solve the differential equation for the deflection curve of beams subjected to distributed loads including dentify and apply appropriate boundary conditions. Use the solution to compute reaction forces, bending moment and shear force distributions.
• Derive and solve the differential equation for axially loaded beams and columns.
  
• Compute the instability load for axially loaded beams.
• Discuss the importance of constitutive equations and apply linear elasticity, thermoelasticity and plasticity models to three dimensional problems.
• Compute principal stresses and corresponding directions.
• Compute stresses and strains on arbitrary surfaces in 2 and 3 dimensional bodies.
  
• Compute stresses and strains in thin-walled pressure vessels.
• Compute effective (equivalent) stresses according to Tresca and von Mises. Apply the corresponding yield criterion to judge the risk of initial yielding and failure.
• Derive and solve the elastic solutions for circular plates and thick-walled cylinders subjected to pressure loads and thermal loads.
• Compute stress concentrations near holes, shoulders, notches etc. by use of handbooks and by the Finite element metod.
  
• Compute stresses and strains in elasticity structures and bodies by use of the finite element method in  ANSYS.
• Use linear fracture mechanics to compute the stress states close to cracks and to judge the risk for crack propagation and failure.
• Describe the principles of fatigue design and master design with respect to high cycle fatigue.
• Use Paris law to estimate the carack propagation and estimate the numbers of load cycles to failure.
• Perform mathematical modelling, i.e., to formulate mathematical equations based on experimental knowledge and judge how accurate this mathematical model is and whether or not a more accurate analysis must be performed.
• Be able to carry out computations and simulations accordingly to engineering ethical codes and standards, i.e., use established physical laws or/and best practise as the basis and to document well.
  
• Be able to identify and discuss ethical dilemmas in the context of strength of materials.
  

• Differential equation for the deflection of beams, tables of beam deformations, method of superposition, statically indeterminate beams.
• Differential equation axially loaded beams. elastic stability and buckling of columns. Euler cases.
  
• Theory of elasticity, principal stresses. equilibrium equations.
• Stress concentrations.
• Thick-walled tubes and circular plates.
•  Fatigue design.
• Introduction to the Finite element method including beam, 2D and 3D structures and calculations of stresses, deformations, buckling loads and life lengths.
  
•  Fracture mechanics.

The course is the second part of three connected courses.
Lecturers, exercises, tutorials, instructions and computer assignments using Matlab and the FE-code ANSYS.

U77b, Institutionen för hållfasthetslära, Chalmers, Göteborg
Handbok och formelsamling i hållfasthetslära, Bengt Sundström (red.), KTH, Stockholm, 1998
Formelsamling i mekanik, M.M. Japp, Inst. för teknisk mekanik, Chalmers.
Introduktion till Hållfasthetslära - Enaxliga tillstånd, Ljung, Ottosen och Ristinmaa, Studentlitteratur, 2007.
Hållfasthetslära - Allmänna tillstånd, Ottosen, Ristinmaa och Ljung, Studentlitteratur, 2007.