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508 ISSN 1392 1207. MECHANICAL. 2012 Volume 18×5): 508516 Complete closed form solution for pressurized heterogeneous thick spherical shells Mehdi Ghana×, Mohammad Mani Nenad** *Mechanical Engineering

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1. Identify the problem: Start by understanding the specific problem or equation that you need to find a closed-form solution for. This could be a mathematical equation, a physics problem, or any other situation that requires a closed-form solution.
2. Analyze the problem: Once you have identified the problem, thoroughly analyze its components and variables. Break down the equation or problem into smaller parts and understand the relationships between them.
3. Use relevant formulas or theorems: Depending on the nature of the problem, utilize the relevant formulas, theorems, or mathematical techniques that are applicable. This could involve simplifying the equation, applying specific rules or identities, or using well-known mathematical solutions.
4. Solve step by step: Proceed to solve the problem step by step, utilizing the techniques and formulas identified in the previous step. Show all the calculations involved and clearly explain each step taken.
5. Simplify the solution: Once you have completed solving the problem, simplify the solution as much as possible. Eliminate any unnecessary terms or factors and simplify the expression to its most concise closed-form solution.
6. Verify the solution: After obtaining the closed-form solution, it is essential to verify its correctness. Double-check each step of the solution, substitute the closed-form solution back into the original equation, and ensure that it satisfies the given problem or equation.

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