## Applying and Interpreting Saint-Venant’s Principle

##### Henrik Sönnerlind January 22, 2018

All structural engineers use Saint-Venant’s principle, whether actively or subconsciously. You can find various formulations of this principle in most structural mechanics textbooks, but its exact meaning is not obvious. Saint-Venant’s principle tells us that the exact distribution of a load is not important far away from the loaded region, as long as the resultants of the load are correct. In this blog post, we will explore Saint-Venant’s principle, particularly in the context of finite element (FE) analysis.

Read More##### Henrik Sönnerlind May 22, 2017

In some applications, particularly within the MEMS field, it is important to study the sensitivity of a device’s eigenfrequencies with respect to a variation in temperature. In this blog post, we show how to do this using COMSOL Multiphysics® version 5.3. We also explore effects like stress softening, geometric changes, and the temperature dependence of material properties.

Read More##### Henrik Sönnerlind May 16, 2017

In some applications, it is necessary to approximate a general 3D stress state by a set of linearized stresses through a cross section of a thin structure. This is important for applications like the analysis of pressure vessels, fatigue analysis of welds, and determination of reinforcement requirements in concrete. In this blog post, we discuss why such an approach is useful as well as how to compute linearized stresses in the Structural Mechanics Module for COMSOL Multiphysics® version 5.3.

Read More##### Henrik Sönnerlind December 5, 2016

In finite element modeling, you may encounter formulations where a force does not monotonically increase with displacement. You can see this property in many material models that include degradation of the material. Such behavior is represented by a negative stiffness. In this blog post, we discuss some examples of negative stiffness, including the physical backgrounds and numerical implications. These ideas are not confined to mechanical analysis, even though the term stiffness originates in that field.

Read More##### Henrik Sönnerlind July 28, 2016

As of COMSOL Multiphysics® version 5.2a, we bring you features designed to enhance your structural mechanics contact modeling. You can, for instance, simulate objects that stick together once they come in contact (adhesion) as well as those that pull apart (decohesion), including full cohesive-zone modeling. Learn how to address each of these scenarios using the new functionality in COMSOL Multiphysics.

Read More##### Henrik Sönnerlind June 27, 2016

Say you are working on a modeling case where loads are moving in such a way that they cross over different mesh elements and boundaries during the simulation. In these cases, among other instances, you may want to apply a boundary condition to only part of the geometrical boundary or only under certain conditions. In this blog post, we’ll discuss how you can utilize the flexibility of COMSOL Multiphysics to handle such situations.

Read More##### Henrik Sönnerlind December 22, 2015

After recently encountering the equations of motion for rotating bodies for the first time, one of my sons came home with a number of interesting questions. His questions brought about a flashback, as I remembered sharing this sense of confusion when studying mechanics many years ago. In today’s blog post, I will present two COMSOL Multiphysics models — one of a gyroscope and one of a spinning top — that illustrate the remarkable properties of rotating bodies.

Read More##### Henrik Sönnerlind September 14, 2015

When performing structural mechanics analyses, you will inevitably encounter the concept of geometric nonlinearity. In this blog post, we discuss what is meant by geometric nonlinearity and when you should take this effect into consideration.

Read More##### Henrik Sönnerlind June 29, 2015

The most fundamental material model for structural mechanics analysis is the linear elastic model. Trivial as it may sound, there are some important details that may not be obvious at first glance. In this blog post, we will dive deeper into the theory and application of this material model and give an overview of isotropy and anisotropy, allowable values for material data, incompressibility, and interaction with geometric nonlinearity.

Read More##### Henrik Sönnerlind June 3, 2015

Your finite element model will sometimes contain singularities — that is, points where some aspect of the solution tends toward an infinite value. In this blog post, we will explore the common causes of singularities, when and how to remove them, and how to interpret results when singularities are present in your model. While most of this discussion is in terms of structural mechanics, similar phenomena can also be found in many other physics fields.

Read More##### Henrik Sönnerlind May 5, 2015

In Part 1 of this blog series, we discussed some of the considerations that you need to make when transforming your measured material data into a constitutive model. Hyperelastic materials were discussed in some detail. Today, we will have a look at how to use nonlinear elastic and elastoplastic materials, and show one way in which you can use your measured data directly in COMSOL Multiphysics.

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