A mixed inverse differential quadrature method for static analysis of constant- and variable-stiffness laminated beams based on Hellinger-Reissner mixed variational formulation

Increasing applications of laminated composite structures necessitate the development equivalent single layer (ESL) models that can achieve similar accuracy but are more computationally efficient than 3D or layer-wise models. Most ESL displacement-based do not guarantee interfacial continuity shear stresses within laminates. A possible remedy is enforcement interlaminar equilibrium in variational formulations, for example, framework Hellinger-Reissner principle, leading to a mixed force/displacement model. In this paper, governing equations bending and stretching beams, comprising only seven stress resultants two displacement functionals, obtained using global fifth-order local linear zigzag kinematics. As strong-form solution technique, differential quadrature method (DQM) an tool which provide excellent convergence with relatively few number grid points. However, dealing high-order equations, conventional DQM incur considerable errors due nature numerical differentiation. Therefore, inverse (iDQM) proposed herein solve fourth-order beams. This approach involves approximating first derivatives functional unknowns, thereby reducing order differentiation being performed. Using non-uniform Chebychev-Gauss-Lobatto point profile, results show predictions improved by iDQM compared DQM. addition, Cauchy’s condition satisfied accurately iDQM, especially vicinity boundaries.