Comparison of weak and strong formulations for 3D stress predictions of composite beam structures

S. O. Ojo*, M. Patni, P. M. Weaver

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

12 Citations (Scopus)


Accurate full field stress responses are often necessary to predict the structural performance of composite structures. The Unified Formulation (UF) is a promising approach to realise efficient and accurate 3D stress predictions of beam-like structures by using recently proposed hierarchical Serendipity Lagrange Elements (SLE) for capturing the 2D response of the beam cross-section while the 1D behaviour along the beam axis is captured using the Finite Element Method (FEM). Despite the computational merits of SLE elements, the performance of UF-SLE-FEM model is strongly influenced by FEM mesh discretisation along the beam's longitudinal axis. With respect to multi-layered beam structures, a high density FEM mesh may lead to loss of efficiency of the UF-SLE-FEM model due to a significant increase in the number of degrees of freedom required to obtain convergence. This study proposes high-order refined formulations of the 1D structure based on strong-form, Differential Quadrature Method (DQM) and weak form, FEM for 3D stress analysis of composite structures. The proposed high-order strong-form DQM and weak-form FEM models, which are benchmarked against exact solutions, lead to significant computational advantages over UF-SLE-FEM models of similar accuracies. However, the symmetry and positive definiteness of the stiffness matrices of FEM models offer a numerical advantage over the strong-form DQM model with non-symmetric, non-positive definite stiffness matrices.

Original languageEnglish
Pages (from-to)145-166
Number of pages22
JournalInternational Journal of Solids and Structures
Early online date24 Jun 2019
Publication statusPublished - 1 Dec 2019

Structured keywords

  • Bristol Composites Institute ACCIS


  • 3D stress
  • Differential quadrature method
  • Higher order finite element
  • Serendipity Lagrange element
  • Unified formulation


Dive into the research topics of 'Comparison of weak and strong formulations for 3D stress predictions of composite beam structures'. Together they form a unique fingerprint.

Cite this