In this paper a new effective formulation of the computation of the statics of elastic bodies in contact isdescribed and demonstrated. Line contact, plane strain, andnegligible friction are assumed. The formulation is an extensionof the standard finite element method (FEM). With theaim to utilise the Hertz theory directly, we use the exactsolution of the elastic 2-dimensional halfspace loaded byHertzian pressure distribution and enforce the contact conditionby the method of Lagrange multipliers. In numericalexamples we have focussed on the demonstration and evaluationof the accuracy of the new formulation for selectedapplications compared with the state of the art node-to-segmentcontact algorithm implemented in the software systemADINA. Proposed formulation ismore accurate for problemswhere Hertz contact dominates the strain state, especially forsmall number of elements, whereas we obtained a fairly goodagreement with ADINAfor a more general bending problem.
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