Derivation of Shape Function Lagrange Method - Finite Element Analysis

TL;DR

Exploring the Lagrange method for deriving shape functions in 2D finite element analysis.

Transcript

so hello and welcome back to the video series of finite element analysis i am bavik soneji and today i am going to talk about the lagrange method for derivation of shape function in 2d problems so let's get started so in the previous video we have seen the satin pdt method to derive the shape function so let's have some recap of it so to derive the... Read More

Key Insights

• 💠 Lagrange method utilizes Lagrange functions for interpolating shape function values in finite element analysis.
• 👻 It allows for the creation of integrated elements with higher degrees of freedom by putting values into polynomial functions.
• 🎨 The method is beneficial for generating shape functions for curved elements, offering versatility in element design.
• #️⃣ Increasing the number of nodes enhances the degree of freedom and complexity in shape function generation.

Questions & Answers

Q: What is the Lagrange method and how does it differ from the Sarinpdt method for shape function derivation?

The Lagrange method uses Lagrange functions to interpolate shape function values, providing a different approach to deriving the relationship between local and natural coordinate systems compared to the Sarinpdt method.

Q: How do the Lagrange functions help in generating integrated elements?

By putting Lagrange function values at different points into polynomial functions, the Lagrange method allows for the creation of integrated elements with higher degrees of freedom, suitable for curved elements.

Q: What role does the number of nodes play in the Lagrange method for shape function derivation?

Increasing the number of nodes in the Lagrange method results in higher degrees of freedom, enabling the generation of complex shape functions for curved elements.

Q: When would one choose to use the Lagrange method over the Sarinpdt method in finite element analysis?

The Lagrange method is preferred when higher degrees of freedom and complex shape functions are needed for curved elements, making it suitable for specialized applications in finite element analysis.

Summary & Key Takeaways

• The Lagrange method involves using Lagrange functions at different points to interpolate shape function values in a 2D problem.

• By putting values at various points and into polynomial functions, the relationship between local and natural coordinate systems is defined.

• This method allows for the generation of integrated elements with higher degrees of freedom and is useful for creating curved elements.