306 Mechanics of Materials 2 9.4 discretisation,calls for engineering judgement in order to model the region as closely as necessary.Having selected the element type,discretisation requires careful attention to extent of the model (i.e.location of model boundaries),element size and grading,number of elements,and factors influencing the qualiry of the mesh,to achieve adequately accurate results consistent with avoiding excessive computational effort and expense.These aspects are briefly considered below. Extent of model Reference has already been made above to applications which are axisymmetric,or those which can be idealised as such.Generally,advantage should be taken of geometric and loading symmetry wherever it exists,whether it be plane or axial.Appropriate boundary conditions need to be imposed to ensure the reduced portion is representative of the whole. For example,in the analysis of a semi-infinite tension plate with a central circular hole, shown in Fig.9.3,only a quadrant need be modelled.However,in order that the quadrant is representative of the whole,respective v and u displacements must be prevented along the x and y direction symmetry axes,since there will be no such displacements in the full model/component. (a)Actual component (b)Idealisation using graded triangular elements 0 (c)Direct stress distribution in y direction across lateral symmetry axis Fig.9.3.Finite element analysis of a semi-infinite tension plate with a central circular hole,using triangular elements. Further,it is known that disturbances to stress distributions due to rapid changes in geometry or load concentrations are only local in effect.Saint-Venant's principle states that the effect of stress concentrations essentially disappear within relatively small distances (approximately306 Mechanics of Materials 2 §9.4 discretisation, calls for engineering judgement in order to model the region as closely as necessary .Having selected the element type, discretisation requires careful attention to extent of the model (i.e. location of model boundaries), eleme~t size and grading, number of elements, and factors influencing the quality of the mesh, to achieve adequately accurate results consistent with avoiding excessive computational effort and expense. These aspects are briefly considered below. Extent of model Reference has already been made above to applications which are axisymmetric, or those which can be idealised as such. Generally, advantage should be taken of geometric and loading symmetry wherever it exists, whether it be plane or axial. Appropriate boundary conditions need to be imposed to ensure the reduced portion is representative of the whole. For example, in the analysis of a semi-infinite tension plate with a central circular hole, shown in Fig. 9.3, only a quadrant need be modelled. However, in order that the quadrant is representative of the whole, respective v and u displacements must be prevented along the x and y direction symmetry axes, since there will be no such displacements in the full t:nodel/component. Fig. 9.3. Finite element analysis of a semi-infinite tension plate with a central circular hole, using triangular elements. Further, it is known that disturbances to stress distributions due to rapid changes in geometry or load concentrations are only local in effect. Saint-Venant's principle states that the effect of stress concentrations essentially disappear within relatively small distances (approximately