H. Bahai

Sensitivity analysis and modification of structural dynamic characteristics using second order approximation

This paper presents a formulation in the form of an inverse eigen value problem for modification of vibration behavior of structures. The proposed method which is based on the second order approximation in Taylor expansion is expressed in terms of variables relating to stiffness or mass matrix parameters in a finite element formulation. An initial sensitivity analysis identifies the regions within the structure where the modifications would yield the required changes in the structures dynamic characteristics. An algorithm is developed which allows efficient modification of structural dynamics characteristics without iterations. These modifications are conducted locally so that only elemental stiffness and matrices are affected. The algorithm is applied to four case studies and it is found that large modification of natural frequencies of up to 10% can be realized with an induced error of less than 5% for truss structures, and less than 3% for plane problems.

A theory of complete force and moment balancing of planer linkage mechanisms

Abstract Tepper and Lowen have shown that complete force balancing of planar linkage is possible using simple counterweights provided that from every point on the linkage there exists a contour to the ground by way of revolute joints only. This paper shows that if a linkage can be fully force balanced using the criterion of Tepper and Lowen, then it can be fully force and moment balanced using geared counter-inertias. Complete mathematical proof of this theory is given.

Active control of natural frequencies of FGM plates by piezoelectric sensor/actuator pairs

An optimization strategy is presented for modifying the dynamic characteristics of functionally graded material (FGM) plates which are actively controlled by piezoelectric sensor/actuator (S/A) pairs. A finite element (FE) model is developed for static and dynamic analysis of FGM plates with collocated piezoelectric sensors and actuators. In this model, the feedback signal to each actuator patch is implemented as a function of the electric potential in its corresponding sensor patch in order to provide active control of the FGM plate in a closed loop system. Using the proposed FE model, a method based on the first-order and second-order approximations in a Taylor expansion is developed to calculate the corresponding changes in the parameters which characterize the piezoelectric patches (i.e. the patch thickness and the feedback gain in each S/A pair) in order to achieve the desired eigenfrequency shifts in the FGM plate. An FGM plate with eight separate S/A pairs is considered as a case study. A sensitivity analysis is initially performed to identify the S/A pairs which have the most influence on the natural frequencies of the plate. The proposed method is used to find a sequence of feedback gains for shifting the natural frequencies to the desired level.

Design optimisation of structures vibration behaviour using first order approximation and local modification

This paper presents an inverse formulation of eigenvalue problem for optimising the dynamics behaviour of structures. The formulation is applied to one- and two-dimensional finite elements which are commonly used in simulation of real structures. Based on this formulation an algorithm is developed for accurate and efficient modification of structures stiffness and mass characteristics to achieve the desired natural frequencies and interpretation of results in terms of physical design parameters. The proposed algorithm is tested by conducting four case studies and the results are validated against exact solutions.

A Finite Element Analysis for Unbonded Flexible Risers Under Torsion

This paper presents a detailed finite-element analysis of unbonded flexible risers. The numerical results are compared to the analytical solutions for various load cases. In the finite-element model, all layers are modeled separately with contact interfaces between each layer. The finite-element model includes the main features of the riser geometry with very little simplifying assumptions made. The numerical model was solved using a fully explicit time-integration scheme implemented in a parallel environment on a 16-processor cluster. The very good agreement found from numerical and analytical comparisons validates the use of our numerical model to provide benchmark solutions against which further detailed investigation will be made.

A parametric model for axial and bending stress concentration factors in API drillstring threaded connectors

This paper presents a study of the variation of stress concentration factor in threaded connectors due to application of external axial and bending loads. The study is based on a hybrid modelling technique previously developed to conduct such analysis. The paper considers the case of API threaded connectors used in drill string applications and uses a particular FEA sub-modelling method of calculating stress concentration factors. The method is used to conduct a parametric study on the effect of geometric thread parameters on axial and bending stress concentration factors.

Hyper-elastic constitutive equations of conjugate stresses and strain tensors for the Seth–Hill strain measures

Abstract The use of hypo-elastic constitutive equations for large strains in nonlinear finite element applications usually requires special considerations. For example, the strain does not tend to zero upon unloading in some elastic loading–unloading closed cycles. Furthermore, these equations are based on objective material time rate tensors, which require incrementally objective algorithms for numerical applications and integration. Hyper-elastic constitutive equations on the other hand do not require such considerations. However, their behaviour for large elastic strains is important and may differ in tension and compression. In the present work, Hyper-elastic constitutive equations for the Seth–Hill strains and their conjugate stresses are explored as a natural generalisation of Hook’s law for finite elastic deformations. Based on the uniaxial and simple shear tests, the response of the material for different constitutive equations is examined. Together with an objective rate model, the effect of different constitutive laws on Cauchy stress components is compared. It is shown that the constitutive equation based on logarithmic strain and its conjugate stress gives results closer to that of the rate model. In addition, the use of Biot stress–strain pairs for a bar element results in an elastic spring which obeys the Hook’s law even for large deformations and has the same behaviour in both tension and compression. The effect of the constitutive equation on the volume change of the material has also been considered here.

A shallow shell finite element for the linear and non-linear analysis of cylindrical shells

Abstract This paper presents a cylindrical strain based shallow shell finite element which is developed for linear and geometrically non-linear analysis of cylindrical shells. The developed element is rectangular inplan and has the only five essential degrees of freedom at each corner node. The displacement fields of the element satisfy the exact requirement of rigid body modes. The efficiency of the element is demonstrated by applying it to the linear and geometrically nonlinear analysis of shell structures. The suitability of the element is also tested for natural frequencies’ calculations of cylindrical shells. Results obtained by the present element are compared with those available in the literature. These comparisons show that efficient convergence characteristics and accurate results can be obtained by using the present element.

Numerical and Analytical Modeling of Unbonded Flexible Risers

This paper presents an analytical formulation and a finite element analysis of the behavior of multilayer unbonded flexible risers. The finite element model accurately incorporates all the fine details of the riser that were previously considered to be important but too difficult to simulate due to the significant associated computational cost. All layers of the riser are separately modeled, and contact interaction between layers has been accounted for. The model includes geometric nonlinearity as well as frictional effects. The analysis considers the main modes of flexible riser loading, which include internal and external pressures, axial tension, torsion, and bending. Computations were performed by employing a fully explicit time integration scheme on a parallel 16-processor cluster of computers. Consistency of simulation results was demonstrated by comparison with those of the analytical model of an identical structure. The close agreement gives confidence in both approaches.

Optimization of the Dynamic Characteristics of Composite Plates Using an Inverse Approach

This article presents an inverse formulation of the eigenvalue problem for computing the required changes in laminated composite plates in order to achieve desired dynamic characteristics in the structure. The stiffness and mass matrices of the plated structure are first derived using the finite element formulation based on the first-order shear deformation theory (FSDT) for laminated composite plates with arbitrary angle-ply stacking sequence. Based on this formulation and using the first- and second-order Taylor expansion both the direct and inverse eigenvalue problems are formulated to find the changes in eigenvalues due to an arbitrary change in physical or geometrical properties of the structure. An initial sensitivity analysis is conducted to identify the layer in which modification of design variables have the most influence on the structures dynamic characteristics. The design variables in this context are defined as the fiber angles in each layer and the layer thickness. The proposed algorithm is applied to several case studies to demonstrate the application and the accuracy of the proposed formulation in solving the direct and the inverse eigenvalue problems with one and two design variables. Dynamic behavior modification of a plate is performed using the inverse approach, and the required modified stacking sequence is obtained to shift the natural frequencies to desired values.