Application Of Differential Equations Method For Solving Statically Determinate Structure

The computer has been highly developed and with a very high popularity. Atthe same time, with the rapid development of it all kinds of calculating softwareis also changed rapidly, and that makes it easier to solve more and more complexmathematical problems, and it also greatly improves the efficiency of calculationas well as analysis."The structural mechanics" is a natural science based on themechanics principle together with a large number of calculating, among them themechanics of determinate structure is the basis for mechanical analysis in everykind of structures. By using computers the work on calculation and analysis ofstructural mechanics will greatly reduce and it provide a method to analyzestatically indeterminate structure as well.At present, the method which is to solve the counterforce through theestablishment of equilibrium equation first, and then calculate the internal forcevalue and show out the diagram is widely used not only in textbooks but alsopractical calculation. This approach can be very intuitive to solve the analysis ofstatically determinate structure mechanics, but it is not convenient for computerprogramming calculation. At the same time, the analysis of the freely supportedbeam bridge is also based on the mechanics analysis method too. This articlemainly introduces a method to make the analysis of statically determinatestructure and freely supported beam-bridge through computer become moreconvenient and simple.In the learning of “structural mechanics” as the ordinary differentialequations is not convenient to calculate so this method is not widely accepted.But method is very simple and also has wide universality, so it is very appropriatefor computer programming calculation. We can use the differential relationship ofthe bending moment, shear force, uniformly distributed load, and angle betweendisplacement to build differential equations and use the force and displacementconstraints determine the undetermined constant coefficient and then determinethe deflection function.to solve the whole issue. Maple has a strong computing ability, especially the symbol processing function is more outstanding, this makesthe use of Maple to build and solve the establishment of ordinary differentialequations become more convenient. And Maple can also draw graphics thismakes the results more intuitive for us. Because of its powerful symbolprocessing, many mechanical quantity can be represented by different symbolsand by changing the values of these symbols we can get different results in theprocess of programming calculation, thus it can greatly simplify the calculationprocedures and improve the computation efficiency either. When we extend thismethod to the analysis of stress analysis of freely supported beam-bridge thecalculation of it will be greatly simplified too.In view of the above content, this paper gives a detailed description. In thefifth chapter of this article I use a freely supported beam bridge as example toexplain how to use Maple to analyze bridge structures with the principle ofsolving ordinary differential equations. And use the result to guide the furtherdesign.