M.D. Olson

Numerical studies of the flow around a circular cylinder by a finite element method

Abstract Numerical solutions of the steady, incompressible, viscous flow past a circular cylinder are presented for Reynolds numbers R ranging from 1 to 100. The governing Navier-Stokes equations in the form of a single, fourth order differential equation for stream function and the boundary conditions are replaced by an equivalent variational principle. The numerical method is based on a finite element approximation of this principle. The resulting non-linear system is solved by the Newton-Raphson process. The pressure field is obtained from a finite element solution of the Poisson equation once the stream function is known. The results are compared with those determined by other numerical techniques and experiments. In particular, the discussion is concerned with the development of the closed wake with Reynolds number, and the tendency of R ≥ 40 flow toward instability.

Review of computing methods for recirculating flows

Abstract A review is presented of the many different finite difference and finite element methods (FDM and FEM) for computing recirculating flows as exemplified by the cavity flow problem. The various methods are categorized according to whether a single integrated system or two segregated, coupled systems are obtained. The integrated schemes appear to be simplest and most efficient, mainly because they satisfy the incompressibility constraint directly in the mean and because the Newton-Raphson method can be used with them. In some cases, the FEM appears to be the most accurate and stable for the same number of unknowns. The method of upwind differencing introduces serious errors in the form of false diffusion which can only be diminished by extreme refinement of mesh sizes. This has to be checked carefully by convergence studies.

Deformation and failure of blast-loaded square plates

Abstract Numerical results for clamped, thin square steel plates subjected to blast loading are presented. The numerical analysis is based on a finite element formulation, which includes the nonlinear effects of geometry and material as well as strain rate sensitivity. A phenomenological interactive failure criterion comprising bending, tension and transverse shear is proposed to predict the various modes of failure. A node release algorithm is developed to simulate the progression of plate rupture from the boundary. The analysis is continued in the post-failure phase to account for the free flight deformation of the torn plate. The predicted failure modes for a blast-loaded plate are presented and compared with previously published experimental data.

Impact analysis of laminated composite plates and shells by super finite elements

Abstract A super finite element method that exhibits coarse-mesh accuracy is used to predict the transient response of laminated composite plates and cylindrical shells subjected to non-penetrating impact by projectiles. The governing equations are based on the classical theories of thin laminated plates and shells taking into account the von Karman kinematics assumptions for moderately large deflections. A non-linear Hertzian-type contact law accounting for curvatures of the colliding bodies is adopted to calculate the impact force . The theoretical basis of the present finite element model is verified by analysing impact-loaded laminated composite plate and shell structures that have previously been studied through analytical or other numerical procedures. The predictive capability of the present numerical approach is successfully demonstrated through comparisons between experimentally-measured and computed force-time histories for impact of carbon fibre-reinforced plastic (CFRP) plates. The current computational model offers a relatively simple and efficient means of predicting the structural impact response of laminated composite plates and shells.

Deformation and failure of blast-loaded stiffened plates

Numerical results for clamped, square stiffened steel plates subjected to blast loading are presented. The finite element formulation, which includes the effects of geometric and material nonlinearities as well as strain rate sensitivity, forms the basis for the numerical analysis. Failure is predicted using an interactive failure criterion comprising bending, tension and transverse shear. A node release algorithm is developed to simulate the progression of rupture. The analysis is continued in the post-failure phase to capture the free flight deformation of the torn plate. The predicted failure modes for a blast-loaded stiffened plate are presented and compared with previously published experimental data. Furthermore, the results of the numerical analysis are used to understand the experimentally observed localized tearing of stiffened plates.

Nonlinear dynamic analysis of blast loaded cylindrical shell structures

Abstract A numerical model for large deflection, elastoplastic analysis of cylindrical sheel structures under air blast loading conditions is presented. The model is based on a transversely-curved finite strip formulation and is capable of stimulating nonlinear transient behaviour of isotropic and stringer-stiffened shells. An implicit time integration scheme and a Newton-Raphson solution technique is employed with a consistent elastoplastic integration algorithm. Numerical verifications of the formulation are carried out by modelling various types of structures under dynamic loadings and comparing the results obtained with other available predictions or experimental results. It is observed that the present model with only one bending mode in the strip direction can predict nonlinear transient response of practical structures with good engineering accuracy.

New finite element results for the square cavity

Abstract New results for the recirculating flow inside a square cavity obtained by a finite element method are presented. The full Navier-Stokes equations in the form of a single, fourth order equation for stremfunction is recast into arestricted variational principles, which form finite element discretization. A triangular element with Hermitian interpolation is used, such that the velocities are continuous and the incompressibility is satisfied exactly. The resulting nonlinear system is solved by Newton-Raphson iteration. Calculations are carried out with several gridworks of progressive show: (1) the convergence of solutions with refinement for fixed Reynolds number R ; and (2) the loss of accuracy with R for fixed gridwork. The range of R covered is from 10 −4 to 3450. The features illustrated include the enlargement of the inviscid core of rigid rotation, the intensification of primary and secondary vortices and the appearance of a third secondary vortex near the upper upstream corner at R =1500 .

Finite element analysis of fibrous composite structures: A plasticity approach

Abstract A finite element program which incorporates a new comprehensive constitutive model for in-plane loading of fibre-reinforced composite (FRC) laminates is presented. This material model combines the classical flow theory of plasticity with a failure criterion to formulate a complete plane stress constitutive relationship for orthotropic FRC laminates up to the ultimate stress condition. Numerical integration of the incremental elastoplastic constitutive equations is based on a tangent predictor-normal return algorithm. The resulting nonlinear equilibrium equations are solved using a full Newton-Raphson iterative scheme. The program is tested for symmetric laminated plates with a central hole and the results are compared against previously published experimental data. Progression of failure in the plane of each layer is also illustrated.

Efficient modelling of blast loaded stiffened plate and cylindrical shell structures

Abstract New modelling methods for stiffened plates and cylindrical shell structures are presented. Rigid-plastic analysis is extended to orthogonally stiffened plates and new efficient finite element and finite strip representations for stiffened plates and cylindrical shells, respectively, are presented. Example numerical results are presented to illustrate the potential of these new methods. Design level accuracy is obtained with relatively simple models which require a minimum of input data and computer-run times.

Nonlinear dynamic analysis of stiffened plates

Abstract A new finite strip formulation for the nonlinear analysis of stiffened plate structures subjected to transient pressure loadings is presented. The effects of large deflections, and strain rate sensitive yielding material properties are included. An explicit central difference/diagonal mass matrix time stepping method is adopted. Example results are presented for an I-beam, an isotropic plate and a five-bay stiffened panel and compared with other predictions and/or experimental results. It is observed that design level accuracy can be obtained for practical structures for a fraction of the cost of full finite element analyses.