Jaroon Rungamornrat

Analysis of Linearly Elastic Inextensible Frames Undergoing Large Displacement and Rotation

This paper presents an efficient semi-analytical technique for modeling two-dimensional, linearly elastic, inextensible frames undergoing large displacement and rotation. A system of ordinary differential equations governing an element is first converted into a system of nonlinear algebraic equations via appropriate enforcement of boundary conditions. Taylors series expansion is then employed along with the co-rotational approach to derive the best linear approximation of such system and the corresponding exact element tangent stiffness matrix. A standard assembly procedure is applied, next, to obtain the best linear approximation of governing nonlinear equations for the structure. This final system is exploited in the solution search by Newton-Ralphson iteration. Key features of the proposed technique include that (i) exact load residuals are evaluated from governing nonlinear algebraic equations, (ii) an exact form of the tangent stiffness matrix is utilized, and (iii) all elements are treated in a systematic way via direct stiffness strategy. The first two features enhance the performance of the technique to yield results comparable to analytical solutions and independent of mesh refinement whereas the last feature allows structures of general geometries and loading conditions be modeled in a straightforward fashion. The implemented algorithm is tested for various structures not only to verify its underlying formulation but also to demonstrate its capability and robustness.

Analysis of planar cracks in 3D elastic media with consideration of surface elasticity

This paper presents an efficient numerical procedure for analysis of arbitrary shaped, planar cracks in a three-dimensional, linear elastic infinite medium by taking the surface elasticity into account. The concept of surface stresses via Gurtin–Murdoch surface theory is integrated with the classical theory of linear elasticity to form a mathematical model capable of simulating cracks under general loading conditions and nano-scale influences. The key governing equations for the bulk material are established in terms of weakly singular displacement and traction boundary integral equations involving only unknowns on the crack face, whereas that for a zero-thickness material layer on each crack face is established in a weak form following the weighted residual technique. The final governing equations for the bulk material and the two crack-face layers are fully coupled via the continuity condition along the interface. The solution of the resulting coupled system is determined numerically by the coupling of a standard finite element procedure and a symmetric Galerkin boundary element method. Owing to the weakly singular feature of all involved boundary integrals, C

Influence of Surface Energy Effects on Elastic Fields of a Layered Elastic Medium under Surface Loading

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Thermo-Electro-Mechanical Behavior of Finite Piezocomposites Cylinder

0 basis functions are adopted everywhere in the approximation of crack-face data and only the special quadrature for evaluating nearly singular and weakly singular double surface integrals is required. Once the implemented numerical scheme is fully tested with existing reference solutions, it is then applied to investigate the role and influence of surface parameters such as the residual surface tension and the in-plane modulus on the near-front field and the size dependency of predicted solutions. Results of several examples under various scenarios are reported not only to demonstrate the capability and robustness of the proposed method but also to indicate the significance of the surface stresses in enhancing the near-surface stiffness and reducing stresses in a local region ahead of the crack front.

Stress Analysis of Three-Dimensional Media Containing Localized Zone by FEM-SGBEM Coupling

A weakly singular, symmetric Galerkin boundary element method capable of solving problems of isolated cracks in three-dimensional, linear anisotropic piezoelectric, infinite media with various types of crack-face boundary conditions including impermeable, permeable, semi-permeable, and the energetically consistent boundary condition introduced by Landis (Int J Solids Struct 41:6291–6315, 2004) is established. The key governing boundary integral equation used in the formulation possesses several crucial features including its desirable symmetric weak-form, weakly singular nature, and ability to treat general material anisotropy, arbitrary crack configurations and any type of boundary condition on the crack surface. The positive consequence of utilizing the singularity-reduced integral equations in the modeling, is that all involved singular integrals can be interpreted in the sense of Riemann and their validity requires only continuous crack-face data allowing

Modeling of Crack Front Singularity in 3D Piezoelectromagnetic Media by Weakly Singular SGBEM

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