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Tangent stiffness matrix
About: Tangent stiffness matrix is a research topic. Over the lifetime, 1031 publications have been published within this topic receiving 21140 citations.
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TL;DR: The tangent modulus factor was derived from the combined theory of strength and stability based on the relationship between stress and strain in a material as discussed by the authors, which can be expressed also by an analytical function with four parameters.
Abstract: A critical step when designing manned deep-sea submersibles is ultimate strength analysis of the pressure shellA method called the tangent modulus factor was appliedIt was derived from the combined theory of strength and stabilityBased on the relationship between stress and strain in a material,the tangent modulus factor curve can be simulated,thus reflecting the structure's balance relationshipThe curve can be expressed also by an analytical function with four parametersThe function was used to calculate the ultimate strength of a titanium alloy spherical pressure shell for a deep-sea submersibleThese results were compared with those from the Taylor Basin formula and the finite element methodThe method proposed in this paper is simpler and the results showed that it produces figures acceptable for engineering practiceThis showed that the tangent modulus factor method is valid for preliminary design and analysis of proposed spherical shell pressure hulls
2 citations
2 citations
TL;DR: Based on the spatial beam-column differential equations, the slope deflection equations considering second-order and bend-torsion coupling effect are established in this paper, where the additional moment caused by torsion and bend deflection are taken into account.
Abstract: Based on the spatial beam-column differential equations, the slope deflection equations considering second-order and bend-torsion coupling effect are established. The additional moment caused by torsion and bend deflection are taken into account. Then the finite element pattern of spatial beam-column considering the couple effect of torsion and bend is given. The tangent stiffness matrix and relevant program for nonlinear analysis are further obtained. By the nonlinear calculation and stability analysis of single component which has high accuracy or precise solution, the precision of the FEM model given in this paper is verified by comparing the results with that given in references.
2 citations
TL;DR: In this paper , a fully nonlinear refined beam element for pre-twisted structures undergoing large deformation and finite untwisting is proposed, which is constructed in the twisted basis to account for geometrical nonlinearity and initial twist.
Abstract: This paper proposes a novel fully nonlinear refined beam element for pre-twisted structures undergoing large deformation and finite untwisting. The present model is constructed in the twisted basis to account for the effects of geometrical nonlinearity and initial twist. Cross-sectional deformation is allowed by introducing Lagrange polynomials in the framework of a Carrera unified formulation. The principle of virtual work is applied to obtain the Green–Lagrange strain tensor and second Piola–Kirchhoff stress tensor. In the nonlinear governing formulation, expressions are given for secant and tangent matrices with linear, nonlinear, and geometrically stiffening contributions. The developed beam model could detect the coupled axial, torsional, and flexure deformations, as well as the local deformations around the point of application of the force. The maximum difference between the present deformation results and those of shell/solid finite element simulations is 6%. Compared to traditional beam theories and finite element models, the proposed method significantly reduces the computational complexity and cost by implementing constant beam elements in the twisted basis.
2 citations
TL;DR: Wang et al. as mentioned in this paper proposed an improved resilient modulus prediction model considering four parameters by introducing k4, which can better adjust the affecting proportion of octahedral shear stress.
Abstract: With the enhancement of transportation speed and axle load, dynamic response of subgrade increases significantly. In order to improve the calculation accuracy of subgrade response under complex stress state, it is necessary to use dynamic indicators instead of static indicators in calculative process. For the sake of investigating the influence factor of dynamic resilient modulus of subgrade silty clay in Eastern Hunan, resilient modulus tests were carried out by conducting repeated load tri-axial tests. Based on available model, an improved resilient modulus prediction model considering four parameters was proposed by introducing k4. Corresponding accurate consistent tangent stiffness matrix was derived. Afterward, the improved model was implemented into finite element method software and verification work was put forward both on single element and pavement-subgrade structure. Finally, calculated results were compared with in-site measured results. Study achievements demonstrate that the improved model exhibits a higher precision and efficiency on single element because k4 can better adjust the affecting proportion of octahedral shear stress. When applied to analysis on pavement-subgrade structure, the improved model can reflect subgrade resilient modulus distribution and evolution more factually. In addition, numerical calculated result nearly coincides with measured results, which shows the application value of the improved model.
2 citations