# Nonlinear Structural Analysis with Finite Element Method

• Hassan2
In summary, Hassan used ABAQUS to analyze problems involving large deformations and contact. It took him a few months to get used to it, and the topic is complex because it requires dealing with elastic-plastic material models, element responses to large deformations, contact between surfaces, and friction. He thinks that his six month estimate is low, and that it would take six years if he is careful to limit the range of problems that software should handle.
Hassan2
TL;DR Summary
Hello everyone.

I need advice from anyone who is experienced with numerical methods of nonlinear structural analysis.

I have several years of experience in developing codes for linear and nonlinear magnetic field analysis. I have some experience with linear structural analysis too. Now I am being asked to develop a commercial code for nonlinear structural analysis but the topic looks complex and frightening!
Unlike in electromagnetics, the nonlinearity of mechanical structures is not only due to the material property. It could be due to large deformation and contact as well. Even though I will be implementing the existing and popular methods, I am still scared and I feel it is not a job that can be done in less than 6 months. Do you have any comments or suggestions?
I have seen some papers and online sources on such topics. Do you know of any comprehensive book that covers the details?

Thank you very much in advance.

Hassan

I used ABAQUS to analyze a range of problems involving large deformations and contact, and it took me a couple months just to learn to properly apply it to my particular problem. The topic looks complex because it is. You need to deal with:

Elastic-plastic material models, including strain hardening and strain rate hardening.
The element(s) must respond properly to large deformations, including deformation where the element is subject to bending.
Contact between surfaces that are initially in contact.
Contact between surfaces that come into contact due to deformation.
Will you model contact only at nodes, or at surfaces?
Friction.
Large deformations may require remeshing. You need built in checks for this.
Provision for element damping to prevent diverging oscillations.
Tensile failure.
And more, that is just what I can think of in a few minutes.

It's been a while, but the ABAQUS manuals that I used were the best software manuals I have ever seen. It's worth reading them just to learn what inputs are needed to solve your class of problems. My recollection is that they had a whole book on their elements, with some detail on the element formulations.

I think that your six month estimate is very low. Six years might be better, and that only if you are careful to limit the range of problems that software should handle. Good luck, because you will need it.

anorlunda
Thank you very much indeed. Your advice clarified many aspects of the job. I need to resist my manager's ambitions then.

jrmichler

## 1. What is the Finite Element Method (FEM)?

The Finite Element Method (FEM) is a numerical technique used to solve problems in engineering and science, specifically in the field of structural analysis. It involves dividing a complex structure into smaller, simpler elements and using mathematical equations to analyze the behavior of these elements under different loading conditions. FEM is commonly used in nonlinear structural analysis to accurately predict the response of a structure to external forces.

## 2. What is nonlinear structural analysis?

Nonlinear structural analysis is a method used to study the behavior of structures that do not follow the linear elastic theory. In other words, it considers the nonlinear behavior of materials and structures under loading conditions that cause large deformations, yielding, and failure. This type of analysis is essential for accurately predicting the performance and safety of structures in real-world applications.

## 3. How is nonlinear structural analysis different from linear structural analysis?

Linear structural analysis assumes that the structure behaves in a linear elastic manner, meaning that the relationship between the applied load and the resulting deformation is linear. Nonlinear structural analysis, on the other hand, takes into account the nonlinear behavior of materials and structures, including plasticity, large deformations, and failure. This makes it a more accurate and realistic method for analyzing complex structures.

## 4. What are the advantages of using the Finite Element Method for nonlinear structural analysis?

The Finite Element Method offers several advantages for nonlinear structural analysis, including its ability to handle complex geometries and boundary conditions, its adaptability to different types of materials and loading conditions, and its ability to provide detailed information about the internal stresses and strains within a structure. Additionally, FEM can be used to optimize the design of structures, reducing costs and improving performance.

## 5. What are some common applications of nonlinear structural analysis with Finite Element Method?

Nonlinear structural analysis with Finite Element Method has many practical applications, including the design and analysis of buildings, bridges, dams, aircraft, and other structures. It is also used in the automotive and aerospace industries to study the behavior of materials and components under extreme conditions. Additionally, FEM is used in biomechanical studies to analyze the response of bones and tissues to external forces.

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