Weighted Residual Method Numerical - Finite Element Analysis | Summary and Q&A

TL;DR

In this video, the Weighted Residue Method is explained through a numerical example, focusing on a solid mechanics problem of a cantilever bar under axial loading.

Key Insights

• 🦾 The Weighted Residue Method is a powerful numerical technique for solving various engineering problems, including solid mechanics, heat transfer, fluid mechanics, and electromagnetic field.
• 👻 The trial solution is a crucial step in the Weighted Residue Method, as it allows for the determination of unknown coefficients.
• 🛄 The weighted residual method aims to minimize the residue, which represents the difference between the governing equation and the trial solution.
• 🖐️ Boundary conditions play a vital role in determining the coefficients and achieving an accurate solution.
• ❓ The Weighted Residue Method provides a systematic approach to solving complex engineering problems by converting them into mathematical formulas.
• 🤢 The deflection of a cantilever bar under axial loading can be determined using the Weighted Residue Method by finding the appropriate coefficients and substituting them into the trial solution.
• 👻 The Weighted Residue Method offers a flexible approach to solving engineering problems by allowing different approaches and variations based on problem requirements.

Transcript

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Questions & Answers

Q: What is the Weighted Residue Method?

The Weighted Residue Method is a numerical technique used to solve engineering problems by minimizing the residue, which is obtained by subtracting the governing equation from the trial solution.

Q: What are the different approaches of the Weighted Residue Method?

The Weighted Residue Method can be approached using Galerkin method, Galerkin approach, collocation approach, and least square method, depending on the problem at hand.

Q: What are the boundary conditions for the cantilever bar problem?

The boundary conditions for the cantilever bar problem are that the deflection at the fixed end (x=0) is zero and the slope of the deflection at the free end (x=l) is zero.

Q: How is the final solution for the deflection of the cantilever bar obtained?

By substituting the determined coefficients and values into the trial solution, which includes the cross-section area, modulus of elasticity, length of the bar, axial load, and variables x and l, the final solution for the deflection of the cantilever bar is obtained.

Summary & Key Takeaways

• The video discusses the Weighted Residue Method and its applications in various engineering problems.

• The problem of a cantilever bar under axial loading is used as an example to illustrate the method.

• The governing equation and boundary conditions for the problem are derived and explained.

• A trial solution is assumed, and the boundary conditions are applied to determine the coefficients.

• The weighted residue method is introduced, and the residue based on the governing equation is set to zero.

• By substituting the determined coefficients and values into the equation, the final solution for the deflection of the bar is obtained.