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Based on the recent advances of hybrid stress finite elements, a series of alternative stress assumptions for these elements are investigated. Several new element models are proposed by using different concepts for the stress interpolation. Under a unified formulation presented in this paper for Hellinger—Reissner principle based hybrid stress element models, the element series 5β‐family for plane stress and 18β‐family for three‐dimensional problems are discussed. The extra incompatible displacements sometimes also added are not introduced in this unified formulation. A number of popular benchmark elastic problems are examined for both two element families. In each family, the element model presented in this paper using normalized transformed higher order stress trials usually gives better predictions than the others.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

We describe how to improve the accuracy of stress in the application of the hybrid finite element method. The idea is based on the fact that the assumed stress hybrid method is equivalent to both the principle of minimum complementary energy within the interior of each element and the principle of the minimum potential energy in the entire domain. It is known that when a good hybrid model is used for the displacement solution, the stress model must satisfy equilibrium within individual elements and be comparable with the boundary displacements. However, the compatibility in the elements is usually ignored and through variational operation it may be only approximately satisfied. So the stress model cannot approach a corresponding analytical stress field. In the present study, after nodal displacements are solved, we propose that a different stress model could be used to find the stress coefficients according to the principle of minimum complementary energy in each element in order to get an improved stress field.

The maintenance of aircraft structure with lower cost is one of the prime concerns to regulatory authorities. The carbon fiber-reinforced polymer (CFRP) patches are widely used to repair the cracked structure. The demands and application of CFRP compel its price to increase in the near future. A distinct perspective of repairing the cracked aluminum panel with the hybrid composite patch is presented in this paper. The purpose of this paper is to propose an alternative patch material in the form of a hybrid composite patch which can provide economical repair solution.

The patch hybridization is performed by preparing the hybrid composite from tows of carbon fiber and glass fiber. Rule of hybrid mixture and modified Halpin–Tsai’s equation are used to evaluate the elastic constant. The stress intensity factor and interfacial stresses are determined using finite element analysis. The debonding initiation load is evaluated after testing under mode-I loading condition.

The hybrid composite patch has rendered the adequate performance for reduction of stress intensity in the cracked panel and control of interfacial stresses in the adhesive layer. The repair efficiency and repair durability of the composite patch repair was ensured by incorporation of the hybrid composite patch.

The studies involving patch hybridization for the application of composite patch repair are presently lacking. The influence of the patch stiffness, methodology to prepare the hybrid composite patch and effects of hybridization on the performance of composite patch repair is presented in this paper.

Poor bending response is a major shortcoming of lower-order elements due to excessive representation of shear stress/strain field. Advanced finite element (FE) formulations for classical elasticity enhance the bending response by either nullifying or filtering some of the symmetric shear stress/strain modes. Nevertheless, the stress/strain field in Cosserat elasticity is asymmetric; consequently any attempt to nullify or filter the anti-symmetric shear stress/strain modes may lead to failure in the constant couple-stress patch test where the anti-symmetric shear stress/strain field is linear. This paper aims at enhancing the bending response of lower-order elements for Cosserat elasticity problems.

A four-node quadrilateral and an eight-node hexahedron are formulated by hybrid-stress approach. The symmetric stress is assumed as those of Pian and Sumihara and Pian and Tong. The anti-symmetric stress components are first assumed to be completely linear in order to pass the constant couple-stress patch test. The linear modes are then constrained with respect to the prescribed body-couple via the equilibrium conditions.

Numerical tests show that the hybrid elements can strictly pass the constant couple-stress patch test and are markedly more accurate than the conventional elements as well as the incompatible elements for bending problems in Cosserat elasticity.

This paper proposes a hybrid FE formulation to improve the bending response of four-node quadrilateral and eight-node hexahedral elements for Cosserat elasticity problems without compromising the constant couple-stress patch test.

This paper aims to consider the heat transportation together with irreversibility analysis for the flow of couple stress hybrid nanofluid past over a stretching surface. The innovative characteristics of this paper include electro-magnetohydrodynamic (EMHD) term, viscous dissipation, Joule heating and heat absorption\omission. The hybrid nanofluid is prepared due to the suspension of the solid nanoparticles of the single wall and multi-wall carbon nanotubes (SWCNTs and MWCNTs) in the blood for the testing purpose of heat transfer and drug deliveries. The experimental value of the Prandtl number used for the blood is 21 from the available literature and very large as compared to the Prandtl number of the other base fluids. Appropriate transformations are incorporated to convert the modeled partial differential equations into the nonlinear ordinary differential equations. The homotopy analysis method (HAM) is used to obtain the solution. The explanation for velocity, energy and entropy are exposed under the influence of various parameters such as E, M, k, Q, S and Ec. The numerical values are calculated and summarized for dimensionless Cf and Nu.

In this investigation, heat transportation together with irreversibility analysis for the flow of couple stress hybrid nanofluid past over a stretching surface is considered. The innovative characteristics of this paper include EMHD term, viscous dissipation, Joule heating and heat absorption\omission. The hybrid nanofluid is prepared due to the suspension of the solid nanoparticles of the SWCNTs and MWCNTs in the blood for the testing purpose of heat transfer and drug deliveries. The experimental value of the Prandtl number used for the blood is 21 from the available literature and very large as compared to the Prandtl number of the other base fluids. Appropriate transformations are incorporated to convert the modeled partial differential equations into the nonlinear ordinary differential equations. The HAM is used to obtain the solution. The explanation for velocity, energy and entropy are exposed under the influence of various parameters such as E, M, k, Q, S and Ec. The numerical values are calculated and summarized for dimensionless Cf and Nu.

The explanation for velocity, energy and entropy are exposed and the flow against various influential factors is discussed graphically. The numerical values are calculated and summarized for dimensionless In addition, the current study is compared for various values of to that published literature and an impressive agreement in terms of finding is reported. It has also been noticed that the and factors retards the hybrid nanofluid flow, while the temperature of fluid becomes upsurges by the rise in these factors.

This is examined while evaluating the previously discussed publications that study on EMHD aspects of magnetized Casson type hybrid nanofluid via entropy generation research is innovative but also acknowledging that the couple stress model challenged bilaterally on stretching surface has not yet been studied. So, there is an ongoing attempt to bridge such a space.

A new laminated composite plate finite element is proposed that is numerically stable and accurate in displacements and stresses, including transverse shear stress. The formulation is based on the Hellinger—Reissner principle with Mindlin kinematics. All stress components are given independent approximations and do not satisfy equilibrium conditions a priori. A novel feature of the formulation is the additive decomposition of the displacement field into two parts corresponding to nodal interpolations and independent local basis functions. The additional basis functions and their associated parameters play an important role in characterizing the accuracy of the element. These functions eliminate shear locking in the lower order elements and provide additional variational constraints on the stresses, leading to very accurate results. A 4‐node and a 9‐node version are developed and it is shown that both elements pass the patch test suggested by Zienkiewicz et al. and are stable in the sense of the Babuška—Brezzi condition. The special structure of the element flexibility matrix provides computational efficiency approaching that of displacement based formulations.

The purpose of this paper is to give a review on the newest developments of high-performance finite element methods (FEMs), and exhibit the recent contributions achieved by the authors’ group, especially showing some breakthroughs against inherent difficulties existing in the traditional FEM for a long time.

Three kinds of new FEMs are emphasized and introduced, including the hybrid stress-function element method, the hybrid displacement-function element method for Mindlin–Reissner plate and the improved unsymmetric FEM. The distinguished feature of these three methods is that they all apply the fundamental analytical solutions of elasticity expressed in different coordinates as their trial functions.

The new FEMs show advantages from both analytical and numerical approaches. All the models exhibit outstanding capacity for resisting various severe mesh distortions, and even perform well when other models cannot work. Some difficulties in the history of FEM are also broken through, such as the limitations defined by MacNeal’s theorem and the edge-effect problems of Mindlin–Reissner plate.

These contributions possess high value for solving the difficulties in engineering computations, and promote the progress of FEM.

A 4‐node, 12‐d.o.f. plate bending element based on the assumed‐stress hybrid formulation is described. The nine stress fields are derived from the 12‐term, Adini—Clough polynomial and the cubic ‘beam shape functions’ are used for the boundary displacements. The element passes the patch test and is invariant to the coordinate system and the node numbering.

The use of enhanced strains leads to an improved performance of low order finite elements. A modified Hu‐Washizu variational formulation with orthogonal stress and strain functions is considered. The use of orthogonal functions leads to a formulation with B (overline) ‐strain matrices which avoids numerical inversion of matrices. Depending on the choice of the stress and strain functions in Cartesian or natural element coordinates one can recover, for example, the hybrid stress element P‐S of Pian‐Sumihara or the Trefftz‐type element QE2 of Piltner and Taylor. With the mixed formulation discussed in this paper a simple extension of the high precision elements P‐S and QE2 to general non‐linear problems is possible, since the final computer implementation of the mixed element is very similar to the implementation of a displacement element. Instead of sparse B‐matrices, sparse B (overline) ‐matrices are used and the typical matrix inversions of hybrid and mixed methods can be avoided. The two most efficient four‐node B (overline) ‐elements for plane strain and plane stress in this study are denoted B (overline)(x, y)‐QE4 and B (overline)(ξ, η)‐QE4.