With the rapid development of computer technology, finite element analysis is more and more used in simulation to solve practical engineering problems. Over the years, more and more engineers, applied mathematicians and physicists have proved that many physical phenomena can be solved by solving partial differential equations, which can be used to describe flow, electromagnetic field, structural mechanics and so on. The finite element method is used to transform these well-known mathematical equations into approximate digital images.
Early finite element mainly focused on a certain professional field, such as stress or fatigue, but generally speaking, physical phenomena did not exist alone. For example, as long as it moves, it will generate heat, which will affect some properties of materials, such as conductivity, chemical reaction rate, viscosity of fluid and so on. The coupling of this physical system is what we call multiple physical fields, which is much more complicated to analyze than analyzing a physical field alone. Obviously, we need a multi-physical field analysis tool.
Before 1990s, due to the lack of computer resources, the simulation of multiple physical fields only stayed in the theoretical stage, and the finite element modeling was limited to the simulation of a single physical field, the most common ones being the simulation of mechanics, heat transfer, fluid and electromagnetic field. It seems that the fate of finite element simulation is the simulation of a single physical field.
This situation has begun to change. After decades of efforts, the development of computational science has provided us with more agile, concise and fast algorithms and more powerful hardware configuration, which makes it possible to simulate multiple physical fields by finite element method. The emerging finite element method provides a new opportunity for multi-physical field analysis and meets the needs of engineers to solve practical physical systems. The future of finite element lies in solving multiple physical fields.
There are countless words. The following examples can only illustrate some potential applications of multi-physical field finite element analysis in the future.
Piezoelectric acoustic transducer can convert current into sound pressure field, and vice versa. This device is generally used for sound source devices in air or liquid, such as phased array microphone, ultrasonic biological imager, sonar sensor, acoustic biological therapeutic instrument and so on. It can also be used in some mechanical equipment such as inkjet printers and piezoelectric motors.
Piezoelectric amplifier involves three different physical fields: structural field, electric field and sound field in fluid. Only software with multi-physical field analysis ability can solve this model.
Piezoelectric material is PZT5-H crystal, which is widely used in piezoelectric sensors. At the interface between air and crystal, the boundary condition of sound field is set as that the pressure is equal to the normal acceleration of the structural field, so that the pressure can be transferred to the air. In addition, due to the influence of air pressure, the crystal domain will be deformed. After applying a current with an amplitude of 200V and an oscillation frequency of 300 KHz, the sound wave propagation generated by the simulated crystal is simulated. The description of this model and its perfect results show that under any complex model, we can express it with a series of mathematical models and then solve it.
Another advantage of multi-physical field modeling is that in school, students intuitively obtain some phenomena that they could not see before, and the simple and easy-to-understand expression has won the favor of students. This is exactly what Dr. Krishan Kumar Bhatia felt when she introduced modeling and analysis tools to senior graduates at Rowan University in Glassboro, new york. His students' theme is how to cool the engine box of motorcycle. Dr bhatia taught them how to judge, find and solve problems with the concept of "design-manufacture-test". Without the application of computer simulation, it is unthinkable to popularize this method in class, because the cost is too high.
COMSOL Multiphysics has an excellent user interface, which enables students to set up heat transfer problems conveniently and get the required results quickly. Dr. bhatia said: "My goal is to make every student understand partial differential equations, so that when they encounter such problems again, they will not worry." "It doesn't need to know too many analytical tools. On the whole, the students said,' This modeling tool is great' ".
Many excellent high-tech engineering companies have seen that multi-physical field modeling can help them stay competitive. Multi-physical field modeling tools allow engineers to conduct more virtual analysis at a time, rather than physical tests. In this way, they can optimize their products quickly and economically. In Medrad Innovations Group in Indonesia, the research team led by Dr. John Kalafut used multi-physical field analysis tools to study the injection process of blood cells in slender syringes, which is a non-Newtonian fluid with high shear rate.
Through this research, Medrad engineers made a new type of equipment called Vanguard Dx angiography catheter. Compared with the traditional sharp nozzle catheter, the new diffusion nozzle catheter makes the distribution of contrast agent more uniform. Contrast agent is a special material, which can show the diseased organs more clearly when shooting X-rays.
Another problem is that the traditional catheter may cause the contrast agent to generate great velocity during use, which may damage blood vessels. Pioneer angiography catheter reduces the influence of contrast agent on blood vessels and minimizes the possibility of blood vessel injury.
The key problem is how to design the nozzle shape of the catheter, which can not only optimize the fluid velocity but also reduce the structural deformation. Kalafut's research team used multi-physical field modeling method to couple the force generated by laminar flow into stress-strain analysis, and then carried out fluid-solid coupling analysis on the shapes and layouts of various nozzles. "One of our interns set up different nozzle layouts for different fluid areas and analyzed them," said Dr. Carafort. "We use these analysis results to evaluate the feasibility of these new ideas, thus reducing the number of times we make solid models."
Friction stir welding (FSW) has been widely used in aluminum alloy welding since 199 1 was patented. The aviation industry first adopted these technologies and is studying how to use them to reduce manufacturing costs. In the process of friction stir welding, a cylindrical cutter with a shoulder and a stirring head rotates and is inserted into the joint of two metals. The rotating shoulder and the stirring head are used to generate heat, but the heat is not enough to melt the metal. On the contrary, softening plastic metal will form a solid barrier to prevent oxygen from oxidizing metal and forming bubbles. The effects of crushing, stirring and extrusion can make the structure at the weld better than the original metal structure, and the strength can even be doubled. This welding equipment can even be used to weld different types of aluminum alloys.
Airbus has funded a lot of research on friction stir welding. Before manufacturers invest and reorganize their production lines on a large scale, Dr. Paul Colegrove of Cranfield University used multi-physical field analysis tools to help them understand the processing process.
The first research achievement is the mathematical model of friction stir welding, which allows Airbus engineers to "see through" the weld to check the temperature distribution and microstructure changes. Dr. Colegrove and his research team also wrote a simulation tool with a graphical interface, so that Airbus engineers can directly extract the thermal characteristics of materials and the ultimate strength of welds.
In the simulation process of friction stir welding, three-dimensional heat transfer analysis and two-dimensional axisymmetric eddy current simulation are coupled. The heat transfer analysis calculates the heat distribution of the structure after the heat flux density is applied to the tool surface. Tool displacement, thermal boundary conditions and thermal properties of welding materials can be extracted. Next, the three-dimensional thermal distribution of the tool surface is mapped to a two-dimensional model. The coupling model can calculate the interaction between heat and fluid during machining.
The electromagnetic, resistance and heat transfer behaviors of coupled substrates need real multi-physical field analysis tools. A typical application is that in the process of semiconductor processing and annealing, there is a hot fireplace using induction heating to grow semiconductor wafers, which is a key technology in the electronics industry.
For example, emery can replace graphite receiver at high temperature of 2000℃, and the receiver is heated by RF device with power close to 10 kW. The design of the furnace cavity is very important for maintaining the uniformity of the temperature in the furnace at such a high temperature. Through the analysis of many physical field analysis tools, it is found that heat is mainly transmitted by radiation. In this model, we can see not only the temperature distribution on the wafer surface, but also the temperature distribution on the quartz tube of the furnace.
In circuit design, the durability and service life of materials are important aspects that affect the selection of materials. The trend of miniaturization of electrical appliances makes the electronic components that can be installed on the circuit board develop rapidly. As we all know, resistors and other components installed on the circuit board will generate a lot of heat, which may lead to cracks at the solder feet of the components and eventually lead to the scrapping of the whole circuit board.
Multi-physical field analysis tools can analyze the heat transfer on the whole circuit board, the stress change of the structure and the deformation caused by temperature rise. This can be used to improve the rationality of circuit board design and material selection.
The improvement of computer ability makes the finite element analysis from single field analysis to multi-field analysis become a reality. In the next few years, multi-physical field analysis tools will bring shock to academic and engineering circles. The monotonous design method of "design-verification" will be gradually eliminated, and virtual modeling technology will make your thoughts go further and ignite the spark of innovation through simulation.
Since 2000, a lot of research has been done on the numerical solution of nonlinear structural problems at home and abroad. The appearance of the modified Newton-Lapson iteration method provides a guarantee for ensuring the calculation accuracy. However, it is still difficult to find the limit point by using this method to solve the ultimate strength of structures. Wright & ampGaylord developed the virtual spring method to ensure the positive definiteness of the structural stiffness matrix after the ultimate strength, and successfully applied it to the analysis of frame structures. Bergan et al. put forward the current stiffness parameter method to suppress the equilibrium iteration in the critical area and then cross the limit point. Batoz put forward the displacement control method, which inverses the internal force of the structure by applying the known displacement change process, so as to obtain the post-ultimate strength response of the structure through the limit point. Riks first proposed the arc length control method, which was improved by Crisfield, Ramm, Powell and Simons in 198 1, and combined with the modified Newton-Lapson method, the problem of "sudden jump" in the post-limit equilibrium path was successfully solved. Gao Suhe and others have studied the relationship between grid division density and finite element solution accuracy. By comparing the calculation results of finite element mechanical models with different grid densities and different element types with the exact solutions, the internal relationship between element grid division and the accuracy of finite element solutions is explored, which is beneficial to determine the reasonable grid density and improve the efficiency of finite element analysis on the premise of ensuring that the finite element solutions meet the actual engineering accuracy requirements. It is proved that for areas with sharp geometric corners and large stress and strain changes, high-order sub-elements should be selected in finite element analysis, and the grid density of elements should be appropriately increased. This can not only ensure the shape of the element, but also improve the precision and accuracy of the solution and accelerate the convergence speed. When automatic meshing, high-order elements are preferred. In grid division and preliminary solution, we should first be simple and then complex, first coarse and then fine. Because engineering structures generally have the characteristics of repeated symmetry or axial symmetry and mirror symmetry, in order to improve the efficiency of solution, we should make full use of the characteristics of repeated symmetry and adopt substructure or symmetrical model to improve the efficiency and accuracy of solution.