| Abstract: | It is customary to use a displacement-based formulation to seek solutions to boundary value problemsfor its computational efficacy. In displacement-based formulations, it is convenient to prescribe the constitutiverelation for stress as an explicit function of displacement gradient. However, from a general theoretical pointof view, the stress and displacement gradient could be related by an implicit function. This study developstechniques to solve boundary value problems when linearized strain and stress are related by an implicitfunction. Here both the stresses and the displacement are taken as unknowns. The stress field is constructed suchthat it satisfies the equilibrium equations identically within the element and the traction continuity requirementsbetween the elements. A continuously differentiable displacement field is constructed, and the linearized strainis computed from this displacement field. Then, the unknown parameters in the stress and displacement fieldare estimated such that the constitutive relation holds in weak integral sense. Though in this procedure thenumber of unknowns has increased in comparison with the displacement formulation, both the strength andserviceability condition can be checked directly without any post-processing. Also, in this procedure, both theequilibrium equations and continuity of displacement are met exactly. The equation that is not satisfied exactlyis the constitutive relation, which is an approximation anyway. The efficacy and accuracy of this method arebenchmarked by studying some standard problems. Planar and three-dimensional truss elements have beendeveloped and benchmarked. Then, a rectangular plane element is implemented and its performance recorded. |
