# Numerical method to solve a spring system

• Ale78
In summary, The conversation discusses the use of a finite element method to solve a deformation model involving a triangle mesh with mass elements and springs. The goal is to find a solution that satisfies the boundary conditions and allows for user-controlled movement of certain vertices. The suggested method is a minimization approach using a finite element method.
Ale78
Hello everyone,
this is my first thread in this comunity.

I explain my problem:

I have a triangle mesh http://en.wikipedia.org/wiki/Triangle_mesh where at every vertex coincide a mass element and on every edge I add a spring.
I would like simulate a deformation model.
But in this article I think to understand that this is a dynamic simulation along the time.
What's I need, is that user move handled vertex in a final position, the remain vertex are free vertex and their final position should be calculate in the way that every spring reach equilibrium.
What's numerical method can solve my problem. Maybe a minimization?

Basically you divide the system into a mesh (as you have) and add the parts of the mesh to form a solution to the system satisfying its boundary conditions.

## 1. How does a numerical method solve a spring system?

Numerical methods use mathematical algorithms to approximate the solution to a spring system. This involves breaking down the system into smaller, simpler parts and using iterative calculations to find an approximate solution.

## 2. What are the advantages of using a numerical method to solve a spring system?

Numerical methods allow for more complex and realistic spring systems to be solved, as they can handle nonlinearities and multiple variables. They also provide a faster and more efficient solution compared to analytical methods.

## 3. What are some common numerical methods used to solve spring systems?

Some common numerical methods include the Euler method, Runge-Kutta methods, and the finite element method. These methods vary in complexity and accuracy, and the choice of method depends on the specific characteristics of the spring system being solved.

## 4. How accurate are the solutions obtained from numerical methods for spring systems?

The accuracy of the solution depends on the chosen method and the number of iterations performed. Generally, the more iterations that are performed, the more accurate the solution will be. However, numerical methods can only provide an approximate solution and may not be exact.

## 5. Can numerical methods be used to solve any type of spring system?

Yes, numerical methods can be used to solve a wide range of spring systems, including linear and nonlinear systems, single and multiple degree of freedom systems, and systems with damping and external forces. They are also applicable to real-world situations and can handle various boundary conditions.

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