How FEA and FEM work together

The finite element method (FEM) And finite element analysis (FEA) Working together , Let engineers know about the structure of a specific design , So that engineers can find weaknesses in artifacts and improve them .

The finite element method （FEM）： stay 20 century 50 A method developed by engineers in the mid-s , The finite element method provides a numerical solution to a complex mechanical problem , It allows a certain degree of error . In general , When a mathematical equation is too complex to be solved in a typical way , You can use the finite element method . A simple way to understand the finite element method is to decompose a large problem into a series of small problems (“ Finite element ”). This makes the whole problem easier . When engineers need to develop an acceptable design that is practical but not necessarily suitable for a particular application , They will use FEM.

Finite element analysis （FEA）： The mathematical equations behind the finite element method are applied to create a simulation , Or finite element analysis (FEA) This thing . This simulation is used for structural analysis , A specific product or design scenario , For example, what happens under the pressure of the real world . The simulation decomposes the whole model into smaller cells in a grid , Engineers use these units to test how different elements of the design interact , And the behavior under simulated stress .

let me put it another way ,FEA It's a virtual model , It helps engineers test specific structural designs , It is usually done by software . A combination of the two ：FEA and FEM Through basic mathematics, it is used to predict the behavior of structures and the integrity of design .

“ In order to understand the physical phenomena happening around us , Complex mathematics is required . This includes fluid dynamics 、 Wave propagation and thermal analysis .”“ Most of these phenomena can be analyzed by partial differential equations , But in the complex case that multiple highly variable equations are required , Finite element analysis is a leading mathematical technique .”

FEA and FEM The advantages of

Improve accuracy and enhance design :FEA and FEM It can improve the accuracy of structural analysis , Because they can deeply understand how the various elements of the design interact in subtle details . They also allow engineers to study the interior and exterior of the design .

Fast and inexpensive testing : because FEM and FEA Allow engineers to create simulated projects , They reduce the need for physical prototypes and tests , This saves time and cost .

FEA and FEM Application

Traditionally ,FEM It is used to test models in aerospace and civil engineering , But now it is expanding to other disciplines , Including biomechanics 、 Thermomechanical 、 Fluid - Structural interaction 、 Biomedical engineering 、 ferroelectric 、 Thermochemistry - Mechanical problems 、 Piezoelectricity and electromagnetism .

FEM The underlying mathematical principles can also be applied to other fields , Such as computational fluid dynamics (CFD) And the thermal dynamics of structures .

“ for example , If you know the temperature of an object at a certain point , How to get a relationship between time and temperature ？” Trevor · Ingrid is 《 Interesting project 》 The magazine says .“ Using finite element analysis , These points can be approximated with different precision modes . For example, a square approximation , A polynomial approximation , And a discrete approximation . Each technology improves accuracy and complexity .”