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Analytical and numerical approaches are used to solve an axisymmetric crack problem with a refined Barenblatt-Dugdale approach. The analytical method utilizes potential theory in classical linear elasticity, where a suitable potential is selected for the treatment of the mixed boundary problem. The closed-form solution for the problem with constant pressure applied near the tip of a penny-shaped crack is studied to illustrate the methodology of the analysis and also to provide a fundamental solution for the numerical approach. Taking advantage of the superposition principle, an exact solution is derived to predict the extent of the plastic zone where a Tresca yield condition is imposed, which also provides a useful benchmark for the numerical study presented in the second part. For an axisymmetric crack, the numerical discretization is required only in the radial direction, which renders the programming work efficient. Through an iterative scheme, the numerical method is able to determine the size of the crack tip plasticity, which is governed by the nonlinear von Mises criterion. The relationships between the applied load and the length of the plastic zone are compared for three different yielding conditions.

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This research aims to study biogas production in King Mongkut's University of Technology North Bangkok Prachinburi Campus. Information of biogas energy from the food waste fermented in 2,000 liters capacity tank was analyzed to determine the heating value in order to calculate the Net Present Value (NPV), Internal Rate of Return (IRR) and Discount Payback Period (DPB). All the measured values from 15 days testing period are the gas quantity of 0.5-0.9 m3 and the average heat value of 10 MJ/m3.Ten fertilization chambers that have capacity of 6,000 liters each for biogas production should be replaced the original size of 2,000 liters tank because using the original tank could not reach breakeven point. By using 10 champers of 6,000 liters capacity each, the payback period has yielded within 5 years and 5 months and given the rate of return 22.48 percent per years throughout 20 years of recovery period.

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