Formulation of hybrid Trefftz finite element method for elastoplasticity

AbstractThe present investigation provides a hybrid Trefftz finite element approach for analysing elastoplastic problems. A dual variational functional is constructed and used to derive hybrid Trefftz finite element formulation for elastoplasticity of bulky solids. The formulation is applicable to either strain hardening or elastic-perfectly plastic materials. A solution algorithm based on initial stress formulation is introduced into the new element model. The performance of the proposed element model is assessed by three examples and comparison is made with results obtained by other approaches. The hybrid Trefftz finite element approach is demonstrated to be particularly suited for nonlinear analysis of two-dimensional elastoplastic problems

Hybrid fundamental solution based finite element method: theory and applications

An overview on the development of hybrid fundamental solution based finite element method (HFS-FEM) and its application in engineering problems is presented in this paper. The framework and formulations of HFS-FEM for potential problem, plane elasticity, three-dimensional elasticity, thermoelasticity, anisotropic elasticity, and plane piezoelectricity are presented. In this method, two independent assumed fields (intraelement filed and auxiliary frame field) are employed. The formulations for all cases are derived from the modified variational functionals and the fundamental solutions to a given problem. Generation of elemental stiffness equations from the modified variational principle is also described. Typical numerical examples are given to demonstrate the validity and performance of the HFS-FEM. Finally, a brief summary of the approach is provided and future trends in this field are identified

Solving potential problems by a boundary-type meshless method-the boundary point method based on BIE

In this paper, a novel boundary-type meshless method, the boundary point method (BPM), is developed via an approximation procedure based on the idea of Young et al. [Novel meshless method for solving the potential problems with arbitrary domain. J Compu

Layout optimization for multi-bi-modulus materials system under multiple load cases

Financial support from the National Natural Science Foundation of China (Grant No. 51179164) and the Australian Research Council (Grant No. DP140103137) is acknowledged

Bone functional remodeling under multi-field loadings

Bone remodeling process is investigated theoretically and numerically within the framework of the extended adaptive elasticity. The coupling between the internal and surface remodeling is considered for the solution of the bone remodeling process. A semi-analytical solution based on the state-space method was used to analyze remodeling process of inhomogeneous bone materials subjected to multi-field loadings. The results show that, in contrast to the former works without considering the coupling between the internal and the surface remodeling, the magnitude of the electrical field changes is obviously lower and the remodeling time is shorten significantly. This implies that the coupling between the internal and the surface remodeling plays an important role in the bone remodeling process

Hybrid graded element model for nonlinear functionally graded materials

A hybrid graded element model is developed in this article for solving the heat conduction problem of nonlinear functionally graded materials (FGMs), whose material properties not only vary spatially but also are temperature dependent. In the proposed approach, both Kirchhoff transformation and iterative method are introduced to deal with the nonlinear term in the heat conduction equation of nonlinear FGMs. Then, the graded element is formulated based on two sets of independent temperature fields. One is the intra-element temperature field, which is defined within the element domain and constructed by a linear combination of fundamental solutions; the other is the frame field, which is defined on the element boundary only and used as the boundary interpolation functions of the element to ensure the field continuity over the inter-element boundary. This model can simulate the graded material properties naturally due to the inherent properties of fundamental solutions, which are employed in constructing the graded element. Moreover, a multi-subdomain method is developed to deal with the problem with different materials. Finally, the performance of the proposed method is assessed by several benchmark examples. The results are in excellent agreement with the analytical solutions

Experimental study of time response of bending deformation of bone cantilevers in an electric field

Bone is a complex composite material with hierarchical structures and anisotropic mechanical properties. Bone also processes electromechanical properties, such as piezoelectricity and streaming potentials, which termed as stress generated potentials. Furthermore, the electrostrictive effect and flexoelectric effect can also affect electromechanical properties of the bone. In the present work, time responses of bending deflections of bone cantilever in an external electric field are measured experimentally to investigate bone's electromechanical behavior. It is found that, when subjected to a square waveform electric field, a bone cantilever specimen begins to bend and its deflection increases gradually to a peak value. Then, the deflection begins to decrease gradually during the period of constant voltage. To analyze the reasons of the bending response of bone, additional experiments were performed. Experimental results obtained show the following two features. The first one is that the electric polarization, induced in bone by an electric field, is due to the Maxwell-Wagner polarization mechanism that the polarization rate is relatively slow, which leads to the electric field force acted on a bone specimen increase gradually and then its bending deflections increase gradually. The second one is that the flexoelectric polarization effect that resists the electric force to decrease and then leads to the bending deflection of a bone cantilever decrease gradually. It is concluded that the first aspect refers to the organic collagens decreasing the electric polarization rate of the bone, and the second one to the inorganic component influencing the bone's polarization intensity.The work was supported by the National Natural Science Foundation of China under Grant No. 11372218