Computational Mechanics is a new discipline based on the theory of mechanics, by using modern electronic computers and a variety of numerical methods to solve the practical problems in the mechanics. It traverses to each branch of mechanics and gradually expands the scope of mechanics research and application in various fields, and gradually develops its own theory and method.
2. Research Content
The application range of computational mechanics has been extended to the fields of solid mechanics, rock and soil mechanics, hydraulics, fluid mechanics, biomechanics, and so on. The computational mechanics mainly studies numerical methods, such as the finite difference method, the finite element method for further research, to explore some new methods and basic theoretical issues. Computational mechanics, which can promote the development of the branches and promote the development of them, are also influenced by them. Finite element method is mainly used in solid mechanics, and the finite difference method is mainly applied to fluid mechanics. In recent years, they are crossing and penetration, especially the application of finite element method in fluid mechanics has become more and more wide.
3. Computational Structural Mechanics
Computational structural mechanics studies the structural analysis and structure synthesis problems in the structural mechanics. Structural analysis refers to the response of the structure under the action of certain external factors, including stress, deformation, frequency, ultimate bearing capacity and so on. Structural synthesis refers to a variety of factors under a certain constraint conditions to optimize the structure design, such as the design of the most economical, the lightest or the maximum stiffness. Computational fluid dynamics mainly studies non viscous flow and viscous flow in fluid mechanics. Non viscous flow includes low speed flow, transonic flow, and supersonic flow and so on; viscous flow includes end flow, boundary layer flow and so on.
4. Research Methods and Characteristics
It generally has the following several steps using computational mechanics to solve various mechanical problems: establish calculation model using the concept and theory of engineering and mechanics; seeking the most appropriate numerical method with mathematics knowledge; calculation program is compiled for numerical calculation and the computer finds out the answer; transports engineering and mechanics concept, judges and interprets the results and significance, make scientific conclusions.
Computational mechanics is adaptable to all kinds of mechanical problems, and has a wide application range. It can give a detailed description of the numerical results, and can be used to describe the mechanical process. It can be repeated several times to carry out numerical simulation, compared with the experimental time and money. However, there are some weaknesses in computational mechanics, for example, it cannot give the analytic expression of the function form, and so it is difficult to show the regularity of numerical solution. Due to the existence and uniqueness of solutions of many nonlinear problems, the numerical results must be verified.
5. Numerical Simulation
The mathematical simulation of mechanical phenomena is often attributed to the solution of ordinary differential equations, partial differential equations, integral equations, or algebraic equations. There are two kinds of methods to solve these equations: one is to find the analytical solution, which is to say, the solution is expressed by the formula; the other is to find the numerical solution. Many problems of mechanics is quite complex, especially complex partial differential equations, it is generally difficult to obtain their analysis solution, and the numerical method is used to solve the operations complicated steps, it consumes a lot of manpower.
6. Difference Method
It is simple, flexible and versatile. When calculating the numerical solution by the difference method, the definition of the independent variable must be "discretized", that is, only attempts the approximate value of the unknown function of the finite point in the domain of the definition of the independent variable.
7. Development Directions
The development of computational mechanics has two directions. One belongs to the application; its main task is to use the existing discretization techniques and numerical methods to prepare the computer's mechanical software, in order to solve the practical problems in engineering technology. Note the tendency is: low price, superior performance of small computers and micro processor appear, some well-known large-scale structural analysis program also in minicomputer to adapt to the needs, and are developing in the mainframe can also on minicomputers running, has a highly modular structure of the program system. The second belongs to the foundation, its main task is the nature of the problems of mechanics and established the computation model, understand the nature of the approximation of the study for numerical methods for these problems and their error, convergence and research on software optimization technology to achieve these methods on computer, etc.