Differential Quadrature Methods in Computational Mechanics
Summary
The differential quadrature method (DQM) is a numerical technique in which derivatives are approximated by weighted linear combinations of function values at discrete grid points. Originating from high-accuracy schemes for partial and ordinary differential equations, DQM has been widely adopted in computational mechanics for the analysis of beams, plates and shells. Its principal advantages are minimal mesh requirements and rapid convergence, offering highly efficient alternatives to traditional finite element or finite difference methods. Extensions such as the generalized differential quadrature method (GDQM) and inverse DQM address complex nonlinearities, high-order derivatives and sensitivity to noise. Combined with variational principles and time integration schemes, these methods have underpinned advances in buckling and vibration analysis, dynamic response under moving loads, nonlocal and size-dependent effects in micro- and nano-scale structures, and viscoelastic materials. Across civil, aerospace and materials engineering, DQM variants deliver robust solutions with reduced computational cost while maintaining rigorous accuracy under diverse boundary and loading conditions.
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Differential Quadrature Methods in Computational Mechanics publication trend
The graph below shows the total number of articles in differential quadrature methods in computational mechanics across all publications each year (not limited to Nature Index journals).
Technical terms
Differential quadrature method: A numerical approach that approximates derivatives by weighted sums of function values at discrete nodes.
Generalized differential quadrature method (GDQM): An extension of DQM accommodating higher-order derivatives and nonlinear or time-dependent formulations.
Inverse differential quadrature method: A variant that reformulates high-order derivative approximations to reduce sensitivity to numerical noise.
Buckling load: The critical compressive load at which a structural element becomes unstable and undergoes sudden lateral deflection.
First-order shear deformation theory: A plate and beam theory accounting for transverse shear strain in moderately thick laminated or composite structures.
References
- Buckling and free vibrations behaviour through differential quadrature method for foamed composites. Results in Engineering (2023).
- Inverse differential quadrature method for structural analysis of composite plates. Computers & Structures (2022).
- Nonlinear Dynamic Analysis of a Curved Sandwich Beam with a Time-Dependent Viscoelastic Core Using the Generalized Differential Quadrature Method (GDQM). Symmetry (2024).
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