Figure 4.11 shows theconfiguration and the division into simple triangular and quadrilateralelements. In this example plane stress conditions are assumed and solution isobtained for both ideal plasticity and strain hardening. This problem wasstudied experimentally by Theocaris and Marketos76 and was firstanalysed using finite element methods by Marcal and King77 andZienkiewicz et al.43 (See reference 5 for discussion on theseearly solutions.) The von Mises criterion is used and, in the case of strainhardening, a constant slope of the uniaxial hardening curve, H, is taken. Data for the problem, from reference 76, are E = 7000 kg/mm2, H = 225 kg/mm2 and σy= 24.3 kg/mm2. Poisson’s ratiois not given but is here taken as in reference 43 as ν = 0.3. To match aconfiguration considered in the experimental study a strip with 200mm width and 360mm length containing a central hole of 200mm diameter. Using symmetry only onequadrant is discretized as shown in Fig. 4.11. Displacement boundary restraintsare imposed for normal components on symmetry boundaries and the top boundary.Sliding is permitted, to impose the necessary zero tangential traction boundarycondition. Loading is applied by a uniform non-zero normal displacementwith equal increments. Displacement elements oftype T3, Q4, and Q9 are used with the same nodal layout. Results for the threeelements are nearly the same, with the extent of plastic zones indicated forvarious loads in Fig. 4.11 obtained using the Q4 element. The load–deformationcharacteristics of the problem are shown in Fig. 4.12 and compared toexperimental results. The strain εyis the peak value occurring at the hole boundary. Thisplane stress problem is relatively insensitive to element type and loadincrement size. Indeed, doubling the number of elements resulted in smallchanges of all essential quantities.