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Purpose The purpose of this study is to propose generalised integral transform technique (GITT) to obtain the exact solutions for bending of clamped parallelogram plate resting on elastic foundation. Design/methodology/approach The GITT is used to solve the bending problem of the full clamped parallelogram plate under an elastic foundation. The auxiliary problem was developed and the corresponding eigenfunction and eigenvalue were calculated simultaneously. The original partial differential governed equation has been represented by the transformed ordinary differential equation system and solved by the subroutine DBVPFD from International Mathematics and Statistics Library. Findings The GITT has been proven to be an efficient approach to solve the bending problem of the plate with different loads, boundary conditions and elastic foundations. The parametric study indicates that the elastic foundation modulus has significant contribution in reducing the vertical deflections and moments for both rectangular and parallelogram plates. With the increasing of aspect ratio (a/b) and the elastic foundation modulus, the trends of the deflection and moment reduction decreased significantly. Originality/value The present hybrid analytical-numerical methodology was first used to solve the mechanics problem of the clamped parallelogram plate resting on elastic foundation. Excellent convergence and high accuracy was observed by comparing with the published results. It exhibits potential application to investigate the mechanics problem of the composite plate with different boundary conditions in the shipbuilding and civil engineering.

Screen pipes collapse failure occurs frequently under formation confining pressure, which seriously affects the oil and gas production. However, the unified equation for calculating collapse strength of screen pipe with different hole arrangement pattern is not find from the literatures. And the corresponding optimization design method was rarely reported. In the present work, finite element models of screen pipes with different hole arrangements are established using the ABAQUS and verified using published experimental results. Then, a unified equation for calculating the collapse strength of screens pipes with different hole arrangement patterns is established based on the numerical simulation results of screens pipes. The geometric characteristics, material properties, and hole arrangement parameters are considered in the present unified equation and the average error of 5.8% was observed compared with the published experimental results. Moreover, the optimization design model for the hole arrangement parameter of screen pipe is implemented based on the nonlinear programming method with multiple constraints. The skin factor of screen pipe is selected as the optimization objective, and the diameter of the hole and the space between holes along the axial and circumferential directions are optimized parameters. The results show that the present optimization design model can obtain the minimum skin factor of the screen pipe with hole arrangement pattern. The corresponding hole diameter and hole space along the axial and circumferential direction were optimized. The screen pipe with staggered and spiral hole arrangement patterns have smaller skin factors than the screen pipe with parallel hole arrangement pattern. The established unified equation and optimization design model can be helpful tools for the initial design of the screen pipe.