Adam Zdunek

Numerical analysis of complex instability behaviour using incremental-iterative strategies

The paper describes how quasi-static, conservative instability problems can be analysed in a multi-parametric space, using generalised path-following procedures for augmented equilibrium problems. ...

A five-field finite element formulation for nearly inextensible and nearly incompressible finite hyperelasticity

A novel Hu-Washizu type 5-field virtual work principle for nearly inextensible and almost incompressible finite hyperelasticity is developed and implemented. The formulation is implemented in an hp-adaptive code providing the proper flexible environment for finite elements with variable order and mixed interpolation. The novel implementation includes residual based error estimation and mesh adaptivity. In the fully constrained limit the formulation provides the constraint manifold setting of hyperelasticity with the simple internal kinematic constraints of inextensibility and incompressibility. A study using a semi-inverse analytical solution and h-refinements and p-enrichments corroborates the convergence characteristics of the 5-field implementation. A new closed form solution for pure torsion of a circular cylindrical tube with inextensible fibres is derived and used for verification. As typical applications are found in e.g. soft tissue biomechanics, passive pressurisation of an ellipsoidal geometry resembling the left ventricle of a rabbit heart is analysed to demonstrate the capability of modelling transversely isotropic materials.

Cavity Radar Cross Section Prediction

Alternative models are discussed for the determination of the interior irradiation contribution to the radar cross section (RCS) of open-ended cavities. Typical applications of practical interest include radiation field prediction of open-ended waveguides and signature prediction of jet engine air intakes and exhaust outlets. It is shown and explained why the classic perfectly conducting (PEC) ground plane (GP) model sometimes predicts measured cavity RCS very poorly. Examples where PEC GP model predictions are 5 dB or more off are provided. Verifications that the used PEC GP model is correctly implemented are provided. A physical optics based modification of the classic PEC GP model is provided and explained. A novel model where the cavity aperture forms an opening in an infinite radar absorbing (IBC) screen is proposed verified and validated. The IBC model resembles the common experimental set-up, and poses an efficient novel halfspace type replacement model approximating a full space setting. The modified PEC GP model or the IBC model can be used interchangeably for cavities with electrically large apertures.

An h-adaptive mortar finite element method for finite deformation contact with higher order p extension

In this work we present a generalization of the mortar segment-to-segment method for finite deformations contact to an h-adaptive version with possible p extension, i.e. using higher order approximation. We recall the main ideas of the mortar algorithm and present the key aspects of adaptivity: error estimation and an h-adaptive strategy. The p extension exploits the feature of the hp-adaptive code in which the contact solver is implemented to handle meshes with nodes of nonuniform orders. We use it to set interior nodes to higher order while leaving linear boundary contact nodes which can be processed by the standard mortar algorithm. Accuracy of elements with low order nodes is restored by adequate subdividing of these elements. Adaptivity and p extension are illustrated with a few numerical tests.

A mixed higher order FEM for fully coupled compressible transversely isotropic finite hyperelasticity

A higher order mixed finite element method is presented for compressible transversely isotropic finite hyperelasticity. The independent variables of the three-field formulation are; displacement, fibre tension and fibre stretch. The formulation admits the description of a fully coupled stress response which evolves from an almost isotropic one into a hyper-anisotropic simply nearly inextensible response with increasing fibre tension, as for example observed in soft tissue biomechanics. Standard displacement approximation of order p in H1(Ω) is used while the auxiliary variables are approximated element wise by square integrable functions of order p−1 in L2(Ω). For finite extensibility the auxiliary variables are statically condensed out yielding a pure displacement based method. It is implemented in an hp-adaptive finite element code. A matching residual based error estimation capability is added and exercised. Numerical evidence indicating stability of approximation is supplied resolving a boundary layer caused by almost inextensible fibres. Coupled and uncoupled stress responses are compared. A generalised compressible transversely isotropic Holzapfel–Gasser–Ogden model is developed for the formulation that intentionally avoids the volumetric–isochoric split. Solutions obtained with the mixed method compare favourably to the corresponding ones obtained with pure displacement formulation. The latter fails in certain strongly anisotropic cases.

Efficient Jet-Engine Inlet Radar Cross-Section Prediction Using Higher-Order Finite-Element Method and Reduced-Order Modeling

Abstract A direct full-wave-based approach and a reduced-order hp-finite-element sub-domain based scattering matrix methodology suitable for calculating the radar cross-section for jet engine air intakes are presented. The convergence of the radar cross-section using uniform mesh refinements and uniform polynomial enrichments are compared. The comparison shows a superiority in favor of the p-enrichments. An efficient method to avoid the bottleneck in the domain decomposition approach at the top level is presented. A very efficient way is to solve the resulting interface problem using the presented reduced-order modeling technique. The radar cross-section can be computed with virtually no loss of accuracy in terms of generalized guided-wave degrees of freedom. The auxiliary generalized scattering matrix approach can also be used without the modal projection or with other generalized inter-facial degrees of freedom to alleviate the interface bottleneck problem.

hp-Adaptive CEM in Practical Applications

A reduced order hp-FE sub-domain based scattering matrix methodology suitable for calculating the Radar Cross-Section (RCS) for electrically huge jet engine air intakes is presented. The efficiency gain in degrees of freedom obtained by using hp-version FEM instead of classical low order h-version FEM is shown to be roughly one order of magnitude. The model reduction achieved by changing from inter-facial FE-d.o.f:s to guided wave participation factors implies another gain in degrees of freedom which becomes very substantial for air intakes with electrically large homogeneous sections. It is shown that the modal reduction can be made without significant loss of accuracy in the cavity-RCS by comparing results obtained using the scattering matrix approach with coupled full wave hp-version finite element-infinite element (FE + IE) and finite element-boundary element (FE + BE) models.

A mixed finite element formulation for slightly compressible finite elasticity with stiff fibre reinforcement. Two fibre families. Uniaxial tension formulation

Abstract We propose a novel finite element based formulation for the solution of the static mechanical mixed boundary value problem of a finite elastic solid reinforced by two distinct, stiff fibre families. The fibre tensions, are assumed decoupled and uniaxial, at out-set. The associated energy conjugate fibre stretch rates are shown to be uniaxial by duality. The natively displacement dependent fibre tension–fibre stretch pairs are replaced by auxiliary independent variables. The complementary, displacement based, stresses and energy conjugate strain rates become tensionless and stretch-rate-less in the two fibre directions, respectively, by construction. An additively decoupled hyperelastic strain energy ansatz in terms of the fibre stretches and a novel apparently doubly stretchless Cauchy–Green tensor is used. The displacement based part of the formulation is set in an apparently inextensible fibre metric space. The proposed uniaxial fibre tension description is statically exact for the fully constrained problem, and the novel doubly stretchless Cauchy–Green tensor is conditionally kinematically admissible in its vicinity. The formulation is realised as a five-field mixed finite element method admitting separate higher order approximations in H 1 , for the displacement, and in L 2 , for the energy conjugate fibre tensions and stretches, respectively. The convergence and correctness of the implementation is verified by numerical and analytical examples.

Inhomogeneous lossy waveguide mode analysis

Abstract This paper discusses electromagnetic numerical mode analysis in waveguides with materially inhomogeneous cross-sections and material dissipation. A full-wave formulation of Maxwell’s homogeneous equations including Gauss electric law, stable at vanishing propagation constant is implemented and verified in terms of the hp -adaptive version of the finite element method. It provides the possibility to use high order polynomial enrichments combined with strongly graded meshes. It is considered most efficient in resolving the loss of solution regularity at material interfaces with large contrast. Numerical examples including materially lossless homogeneous and inhomogeneous cross sections with and without losses are analysed to corroborate the implementation. The efficiency of using higher order polynomial enrichments is shown. The approach is anticipated to have a broad application, from modern on-chip interconnect and antenna technologies to the design of low observable aerial vehicles.

Application of an hp-adaptive FE method for computing electromagnetic scattering in the frequency domain

Herein the electromagnetic scattering is determined using the finite element method. In particular the radar cross section of the scatterer is estimated. Comparison between the finite element method (FEM), method of moments (MoM) and the method of physical optics (PO) is made in one numerical example. In another numerical example, the convergence rate is compared using pure h-refinement, p-enrichment and with a priori hp-adaptive refinements. The gain using the hp-adaptive approach is significant since an exponential convergence may be obtained.