Symmetric Boundary Conditions in FEA

Key Takeaways

• FEA uses a numerical technique called the finite element method (FEM) to simulate any given physical phenomenon. 

• The accuracy of FEA depends on mesh generation and the application of the right boundary conditions.

• Symmetric boundary conditions are constraints that are used for stabilizing the finite element model.

For accurate predictions of the functional behavior of a system in electronics, finite element analysis (FEA) is performed. FEA simulation includes the real geometry and electromagnetic properties in the simulation model and the physical effects of forces, heat transfer, and vibrations are analyzed in this model.

In FEA, the physical domain under analysis is subjected to constraints, called boundary conditions, for convergence of the solution to reasonable results. Symmetric boundary conditions in FEA are constraints capable of reducing the use of computational memory and simulation time. We will discuss FEA and its symmetric boundary conditions in this article. 

Finite Element Analysis

When you want to see how a product reacts to physical effects such as forces, vibrations, fluid flow, heat, etc. before development, then finite element analysis (FEA) is the computational method you should rely on. FEA uses a numerical technique called the finite element method (FEM) to simulate any given physical phenomenon. FEA depends on mathematical models to analyze the effects of physical conditions on a system. FEA simulations are conducted with the help of specialized software that has FEA algorithms integrated into it. FEA software helps engineers optimize designs, which leads to the development of better products. It reduces the need for physical prototyping and experiments and saves a lot of time and money. 

FEA Software

In FEA software, the system or structure where FEA is applied is divided into millions of small elements that are collectively called mesh. Each of these elements is subjected to mathematical calculations. The individual results corresponding to each element are combined to give the final result. As the calculations are done on the mesh, some interpolations are needed. These approximations are made within the boundary of the physical system. There are points in the mesh where the data is known mathematically. Such points are called nodal points and are found at the boundary of the elements, known as boundary conditions.

Boundary conditions are significant when building a finite element model and performing FEA. The accuracy of the FEA depends on mesh generation and the application of the right boundary conditions. 

Boundary Conditions in FEA 

It is easy to run FEA, but difficult to produce reasonable results from FEA simulation. The most common issue that leads to no results from FEA is boundary conditions. Generally, FEA deals with physical phenomena that are mathematically expressed as ordinary differential equations or partial differential equations. Most of these problems are boundary value problems. 

Boundary Value Problems

A boundary value problem consists of a set of differential equations to be solved in a region where the boundary conditions are known. These boundary conditions act as constraints that are essential for solving boundary value problems. 

The Importance of Boundary Conditions

Boundary conditions are significant in resolving computation problems utilizing FEA. A wrong choice of boundary condition can lead to either divergence of the solution or convergence to the wrong solution. The choice of applying the right realistic boundary condition is important to avail the full potential of FEA. 

Types of Boundary Conditions

There are different types of boundary conditions that can be applied to the boundaries of the physical domain. There are many types of boundary conditions, including:

• Dirichlet boundary condition

• Neumann boundary condition

• Robin boundary condition

• Cauchy boundary condition

Depending on the symmetry in the finite element model, symmetric boundary conditions also exist in FEA. 

Symmetric Boundary Conditions in FEA

The symmetric plane boundary condition can be applied in models where there is a symmetric plane. When there is symmetry in the finite element model, the physical size can be reduced to one-half. The system can be studied using the reduced model, as the other half is identical and obeys anything that applies to the reduced model under analysis. With the application of symmetric boundary conditions, the size of the problem simulated is reduced and takes less amount of memory and time to achieve reasonable results.

There are two variants of symmetry—along a plane of geometric symmetry or electrical symmetry. The structure modeled in FEA can have electrical symmetry in two variants—electric field symmetry and magnetic field symmetry.

The co-planar microstrip and co-axial cables are two examples where symmetric boundary conditions can be applied. In co-planar microstrip pairs, there is electric field symmetry. In the co-axial cable model, there is magnetic field symmetry. The complexity and size of the design are reduced by applying symmetric boundary conditions, which shortens the solution time in problems involving co-axial and co-planar microstrips.

Symmetric boundary condition constraints can stabilize the finite element model. The application of symmetric boundary conditions reduces the model size and makes FEA analysis simpler than full model FEA. Using finer mesh in a reduced analysis model can also result in a more accurate solution compared to that from a coarsely meshed full model. Cadence software can support finite element modeling for calculating the behavior of a system under analysis. 

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