Solid Mechanics, Fluid Mechanics, And Management Aspects Of Algebraic Explicit Analytical Solution

.Analytical solutions have irreplaceable theoretical vaules. Many analytical solutionshave played important roles in the early development of some discplines. In addition to theirtheoretical meanings, analytical solutions can also be used to check the accuracy, convergenceand effectiveness of all kinds of numerical computation methods and to optimize theirdifferencing schemes, grid generation ways and so on. This is because analytical solutions canexpress exactly the specifical situation of one equation under certain initial and boundaryconditions. Therefore, the function of analytical solutions are not to be ignored in despite ofthe various computational discplines. Algebraically explicit analytical solutions (not includeparticular functions and infinite series in solutions)are especially suitable for theoreticalresearch and to be applied to check numerical calculations as benchmark solutions. Even so,algebraically explicit analytical solutions covered in open literatures are very few up to now,on account of mathematical difficulties in accordance with analyzing partial differentialequations. The dissertation researches algebraically explicit analytical solutions of soliddynamics, hydrodynamics, administration and so on. Using their basic equations to analyseproblems concerning their processes, even to create and renew them. The main contents are asfollows: analytical solutions of ideal plasticity, axisymmetrical 2-D analytical solutions ofideal plasticity, analytical solutions of porous medium dynamics, analytical solutions ofelasticity dynamics including body force, some concise exact analytical solutions ofrectangular plate bending, some concise exact analytical solutions for bending of rectangularplate with a pair of parellel free edge, some concise exact analytical solutions offour-dimensional energy demanding systerm, analytical solutions of energy demandingsubsystem and unsteady 1D exact solutions of non-Darcy flow in post-failure rock.