By D.R. Owen
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Additional resources for Finite elements in plasticity: theory and practice
On increasing the load further, the material is assumed to exhibit linear strain-hardening, characterised by the tangential modulus, ET. At some stage after initial yielding, consider a further load application resulting in an incremental increase of stress, do, accompanied by a change of strain, de. A s s u e - t h a t the strain can be separated into elastic and plastic ONE-DIMENSIONAL N O N L I N E A R PROBLEMS Elastic behaviour Slope, E Y I ' I I Strain. c Fig. 9 Elastic, linear strain-hardening stress-strain behaviour for the uniaxial case.
Also initialise the arrays for locating and recording prescribed values of the unknown. DATA 48-61 Read and write the node number and prescribed value for each degree of freedom for each boundary node and store in the global arrays IFPRE and PEFIX. DATA 62-71 Read and write the nodal loads for each element. 3 Subroutine NONAL The main function of this subroutine is to control the solution process according to the value of the solution algorithm parameter, NALGO, input in subroutine DATA. The subroutine sets the value of indicator KRESL to either 1 or 2 according to NALGO and the current value of the iteration number IITER and increment number IINCS.
19b) gives R, = -46113 immediately. 19a) since 42, $3, $4 are known at this stage. This gives = 179/13. Since the above procedure is quite systematic it can be readily programmed. The global stiffness matrix must be assembled and the stiffness equations reduced only if the element stiffnesses have been changed for the current iteration. INEAK I'IIOBLEMS 49 KRESL = I, but only the global load vector need bc formed and reduced if KRESL = 2. In this way a considerable number of arithmetic operations are avoided if only equation resolution is to be undertaken.