A comparative study of shape imperfection and internal pressure effects on plastic, shakedown and elastic limit loads using large and small strain formulation of 90° pipe bends

The present work quantifies the effect of ovality and wall thinning on plastic, shakedown and elastic limit load of pipe bends under cyclic in-plane closing bending load and internal pressure. Three-dimensional finite element analyses with large strain (geometric nonlinear analysis) formulation was performed by considering the pipe bend material to be elastic-perfectly plastic. Plastic limit loads are determined from the plot of reaction moment versus angular rotation curve. Abdalla's simplified technique (ST) was used to calculate elastic and shakedown limit loads. The presence of ovality shows significant effect on plastic, shakedown and elastic limit loads and their boundaries for all the models. Thinning has minimal effect on plastic limit loads for large strain analysis while it has a remarkable effect on elastic and shakedown limit loads for ovality up to 5%. Experimental plastic limit moments in open literature was used to validate the present finite element (FE) plastic limit loads. Plastic, shakedown and elastic limit boundaries of large strain analysis or geometric non linear (GNL) analysis were compared with the respective boundaries of small strain analysis or Geometric linear (GL) analysis. Mathematical equations are formulated to express the generated limit moment boundaries for shape imperfect pipe bends.