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The aim of the present study is to investigate the effect of surface melting using tungsten inert gas (TIG) welding process and rapid solidification on the microstructure and hardness of Ni-free biomedical Co–28Cr–5Mo-0.3%C alloy. The microstructural studies revealed that surface melting via TIG welding process results in uniform distribution of the nano-sized M 23 C 6 carbides in the range of 10–100 nm at γ-fcc/e-hcp interface. It was found that the volume fraction of the athermal martensite plays a key role on the size of the finely dispersed nano-sized M 23 C 6 carbides at γ-fcc/e-hcp interface. The hardness of TIG-treated surface was found to be greater than as-cast alloy which could be attributed to the dispersion of the nano-sized carbides at γ-fcc/e-hcp interface as well as higher volume fraction of athermal martensite.

This paper proposes an inverse strategy for relocation of structural natural frequencies using first order formulation and solution algorithm. In the proposed method a sensitivity analysis of the systems eigenvalues with respect to material or geometrical parameters of the structure is conducted initially. The required parameter variation to achieve a desired frequency shift for the structure is then computed. The proposed technique incorporates the design constraints or objective functions in the system equations in such a way that a square system of equations is always preserved. The formulations are general and applicable to all finite element structures because the sensitivity analysis is based on the stiffness and mass matrices regardless of the type of elements used. An algorithm suitable for implementation of the technique for practical purposes is developed. The accuracies of the proposed methods are tested conducting several case studies and the results are validated against exact solutions.

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.

In this paper, general relations between two different stress tensors T f and T g , respectively conjugate to strain measure tensors f ( U ) and g ( U ) are found. The strain class f ( U ) is based on the right stretch tensor U which includes the Seth–Hill strain tensors. The method is based on the definition of energy conjugacy and Hill’s principal axis method. The relations are derived for the cases of distinct as well as coalescent principal stretches. As a special case, conjugate stresses of the Seth–Hill strain measures are then more investigated in their general form. The relations are first obtained in the principal axes of the tensor U . Then they are used to obtain basis free tensorial equations between different conjugate stresses. These basis free equations between two conjugate stresses are obtained through the comparison of the relations between their components in the principal axes, with a possible tensor expansion relation between the stresses with unknown coefficients, the unknown coefficients to be obtained. In this regard, some relations are also obtained for T (0) which is the stress conjugate to the logarithmic strain tensor ln U .

This paper presents formulations for inverse optimisation of vibration behaviour of finite element models of both truss and continuous structures. The proposed algorithms determine the required modifications on truss and continuous structures to achieve specified natural frequencies. The modification can be carried out globally or locally on the structures stiffness and matrices and the formulation can also be used to add new structural members to achieve the desired response. Numerical examples and finite element implementation of the developed method are provided to demonstrate the feasibility of the formulations.

This work presents the details of a finite element-based numerical method to analyse general contact/impact problems, called united elements method (UEM). In contrast to usual methods, that is Lagrange Multipliers and Penalty Function, this method is conceptual, suitable for computer programming, and free from inherent deficiencies of those methods. The key points of this procedure are elimination of the normal degree of freedom of the contactor node from the system energy potential functional in terms of target surface motion, and proper calculation of target element unbalanced forces, to incorporate the contact constraints. After a review on classic formulations, the mathematical and matrix presentation of the united element stiffness matrix are discussed. Solution of some examples adopting a Newton–Raphson-based solution, together with a normal return scheme, support the capability and accuracy of the procedure in static and dynamic problems.

In this paper, conjugate stresses of the Seth–Hill strain measures are treated by means of the definition of energy conjugacy and Hill’s principal axis method. This approach results in relations between components of two different conjugate stress tensors. The results are valid for distinct as well as coalescent principal stretches. Illustrative examples are solved to demonstrate the simplicity and usefulness of the derived relations between conjugate stress tensors.

In this paper, a solution method is presented for the analysis of contact/impact between deformable bodies. The method is different from Lagrange multipliers and Penalty methods. Having defined a body as contactor and the other as target, it is assumed that contact forces are developed between contactor nodes and target surface. The method is based on stiffness transformation and eliminating the normal degree of freedom of contactor node. The method is absolutely general and can be used in static and dynamic nonlinear problems. All the drawbacks of Lagrange multipliers and Penalty method are vanished in this technique and it can be easily implemented in computer programs. The efficiency and applicability of the method is demonstrated by several illustrative examples.

In this paper, a finite element method is presented in details to solve a nonlinear partial differential equation with mixed boundary conditions which has many applications in engineering fields. Numerical examples are given to demonstrate the accuracy and efficiency of the method. Comparison of results, using analytical and numerical solutions, reveals a very good agreement between two methods.