Rayleish Ritz Method with Different Trail Functions

TL;DR

Ritz method is used to solve the deformation of an axially loaded bar, with different trial functions giving varying levels of accuracy.

Transcript

click the bell icon to get latest videos from equator hello welcome to finite element methods so let us learn the relegates method with different trial functions so what if I take a trial function as a constraint as a linear as a quadratic as a cubic I can't take any trial function right so what are the different pile functions we can put it in the... Read More

Key Insights

• 😒 The Ritz method uses trial functions to approximate displacement and stress in structural analysis.
• ❓ Trial functions must satisfy essential boundary conditions to provide accurate solutions.
• ❓ The choice of trial function, such as the degree of the polynomial, affects the accuracy of the approximated solution.

Questions & Answers

Q: What is the purpose of using trial functions in the Ritz method?

Trial functions are used to approximate the displacement and stress of a structure by satisfying essential boundary conditions.

Q: Why is it necessary for trial functions to satisfy essential boundary conditions?

Trial functions must satisfy essential boundary conditions to ensure that the approximate solution is valid and accurate.

Q: Why is a polynomial of degree 0 not a suitable trial function?

A polynomial of degree 0, which corresponds to a constant displacement, does not satisfy the essential boundary condition and does not provide an accurate solution.

Q: Why is a polynomial of degree 3 preferred for this problem?

A polynomial of degree 3 provides a cubic displacement, which matches the exact solution for the problem and gives a more accurate approximation.

Summary & Key Takeaways

• The Ritz method is used to solve the deformation of an axially loaded bar with different trial functions.

• Trial functions must satisfy essential boundary conditions to be valid.

• Polynomial trial functions of varying degrees are used to approximate the displacement and stress.