ottosen petersson introduction to the finite element method 1992

Ngày tải lên: 23/10/2013, 15:46

... squares method and the Galerkin method give the same equations. Furthermore, the solution of the Galerkin and least squares methods would be the same as that of the Ritz method. For the collocation method, ... e 5 3 4 6 1 ã ã ã ã ã ã ã ã 54 AN INTRODUCTION TO THE FINITE ELEMENT METHOD Problem 4.6: Consider the hydraulic pipe network (the flow is assumed to be laminar) shown in Fig. P4.6. Write the condensed equations for the unknown pressures ... AN INTRODUCTION TO THE FINITE ELEMENT METHOD ♠ New Problem 2.1: The instructor may assign the following problem: d dx (1 + 2x 2 ) du dx á + u = x 2 (1a) u(0) = 1 , à du dx ả x=1 =2 (1b) The...

Ngày tải lên: 08/04/2014, 10:38

... fall into this category. It is thus dicult to determine the origins of the đnite element method and the precise moment of its invention. Table 1.1 shows the process of evolution which led to the ... factor ignored in this formulation because the energy contribution is limited to the elements themselves. However, if, in the limit, as the size of the subdivision decreases continuity is restored, ...  r 1 F F F r n 8 > < > : 9 > = > ; 1:8 applied at the nodes in addition to the distributed loads applied to the individual elements. Again, any one of the forces r i must have the same number of components as that of the element reactions...

Ngày tải lên: 14/03/2014, 15:20

... of the general đnite element procedures available in Volume 1 may not be familiar to a reader intro- duced to the đnite element method through dierent texts. We therefore recommend that the ... that Volume 2 can be used by investigators familiar with the đnite element method in general terms and will introduce them here to the subject of specialized topics in solid mechanics. This volume ... by a đnite element method we always need to solve a set of simultaneous algebraic equations of the form Ka  f 2:1 Provided the coecient matrix is non-singular the solution to these equations...

Ngày tải lên: 14/03/2014, 15:20

... calculus (FIC) method and indeed to other methods suggested dealing with the problems of steady- state equations. For the transient solutions the obvious đrst approach would be to try again the same ... is to separate the ¯uid mechanics formulations and applications from those of solid mechanics and thus perhaps to reach a dierent interest group. Though the introduction to the đnite element method ... most of the ¯uid mechanics problems lie. The present volume is devoted entirely to ¯uid mechanics and uses in the main the methods introduced in Volume 1. However, it then enlarges these to deal...

Ngày tải lên: 14/03/2014, 15:20

... m g is the mass of the gas in the bulb; c pg , the specific heat of the gas; m w ,themass of the wall of the bulb; c pw , the specific heat of the wall; h f , the heat transfer coefficient between the ... h p is the heat transfer coefficient from the metallic part to the gas; A p , the surface area of the metallic part in contact with the gas; h g , the heat transfer coefficient of the gas to the wall; ... A g , the surface area of the gas in contact with the wall; h w , the heat transfer coefficient from the wall to the atmosphere; A w , the wall area in contact with the atmosphere;  p and  w , the...

Ngày tải lên: 17/03/2014, 13:53

... thus perhaps to reach a dierent interest group. Though the introduction to the đnite element method contained in the ®rst volume (the basis) is general, in it we have used, in the main, examples ... calculus (FIC) method and indeed to other methods suggested dealing with the problems of steady- state equations. For the transient solutions the obvious đrst approach would be to try again the same ... and obeys the gas laws which relate the pressure to temperature and density. It is now necessary to add the energy conservation equation to the system governing the motion so that the temperature can...

Ngày tải lên: 22/03/2014, 11:20

Ngày tải lên: 29/03/2014, 02:20

... where the integral form holds. Therefore one has to go back to the integral equation and derive suitable jump conditions to hold at the discon- tinuities and incorporate them back into the weak ... guide refinement strategies for adaptive finite element methods, and for other purposes. We will return to this topic later, after introducing the finite element discretization in Chapter 2. a(v, ... approximation of the time-independent value Au(0, t) plays a key role in the finite volume schemes. Let us stop the comment at this point, since the finite volume method lies beyond the scope...

Ngày tải lên: 31/03/2014, 15:57

Ngày tải lên: 08/04/2014, 10:29

... intended to augment this short introduction to the historical background. The modern development of the finite element method began in the 1940s in the field of structural engineering with the work ... Before the development of the finite element method and the computer, even this relatively simple problem took many hours to solve. The next illustration of the application of the finite element method ... ele- ments. The line elements are the simplest of elements to consider and will be discussed in Chapters 2 through 5 to illustrate many of the basic concepts of the finite element method. The basic...

Ngày tải lên: 08/04/2014, 10:35

... discretized into small elements. In each of these elements, the profile of the displace- ments is assumed in simple forms to obtain element equations. The equations obtained for each element are then assembled ... limit. The critical time step t cr should be the time taken for the fastest stress wave in the solids/structure to cross the smallest element in the mesh. Therefore, the time steps used in the ... into detail that the mathematical foundation of all these three approaches is the residual method. An appropriate choice of the test and trial functions in the residual method can lead to the...

Ngày tải lên: 08/04/2014, 10:38

Ngày tải lên: 04/06/2014, 13:17

Ngày tải lên: 27/06/2014, 17:20

Ngày tải lên: 27/06/2014, 17:20

Ngày tải lên: 27/06/2014, 17:20

Ngày tải lên: 27/06/2014, 17:20