Results 101 to 110 of about 167 (141)
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Uniqueness for plane crack problems in linear elastostatics
Journal of Elasticity, 1973This paper contains a proof of the uniqueness of solution to the traction boundary value problem in linear elastostatics for a bounded domain containing a crack. Attention is restricted to the two-dimensional case, but the elastic material considered need not be homogeneous or isotropic.
J. K. Knowles, T. A. Pucik
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Introduction to the finite element method for linear elastostatics
2020Abstract This chapter introduces the widely-used finite element method applied to solving two-dimensional boundary value problems in linear elastostatics under plane strain or plane stress conditions. While the chapter illustrates the main structure of the finite element method using the equations of linear elasticity, the method can ...
Lallit Anand, Sanjay Govindjee
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Solutions to some classical problems in linear elastostatics
2020Abstract This chapter presents and discusses the solution of several classical problems in linear elastostatics, including thick-walled spheres and cylinders under external and internal pressure; bending and torsion of prismatic bars of arbitrary cross section; and the use of Airy’s stress function method to solve several two-dimensional
Lallit Anand, Sanjay Govindjee
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On a class of conservation laws in linearized and finite elastostatics
Archive for Rational Mechanics and Analysis, 1972Several years ago ESHELBY [1] (1956), in a paper devoted to the continuum theory of lattice defects, deduced a surface-integral representation for the "force on an elastic singularity or inhomogeneity", which-in the absence of such defects-gives rise to a conservation law for regular elastostatic fields appropriate to homogeneous but not necessarily ...
Knowles, J. K., Sternberg, Eli
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Sensitivity analysis for non‐linear constrained elastostatic systems
International Journal for Numerical Methods in Engineering, 1992AbstractAdjoint and direct differentiation methods are used to formulate design sensitivities for non‐linear constrained elastostatic systems. Variations of a general response functional are expressed in explicit form with respect to all design field variations, including shape.
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ON THE MAXIMUM MODULUS THEOREM IN LINEAR ELASTOSTATICS FOR EXTERIOR DOMAINS
Mathematical Models and Methods in Applied Sciences, 1996This paper deals with the system of linear elastostatics in exterior three-dimensional domains. We prove that the modulus of every solution with finite energy of such a system may be majorized by a positive constant times the maximum value of the modulus of the Dirichlet data at the boundary (maximum modulus theorem).
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The Existence and Uniqueness of Solutions by the Covering Domain Method in Linear Elastostatics
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1996AbstractThe paper deals with problems of linear elastostatics with multiply connected solution domains. Generally, a multiply connected domain can be represented in a non‐unique way by the intersection set of n > 1 domains, each of which covering completely the original solution domain.
Lin, X., Ballmann, J.
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Spatial energy distribution in non-linear elastostatics
International Journal of Engineering Science, 1994zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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SOME DECAY AND OTHER ESTIMATES IN TWO-DIMENSIONAL LINEAR ELASTOSTATICS
The Quarterly Journal of Mechanics and Applied Mathematics, 1988It is considered a simply connected region R in the \((x_ 1,x_ 2)\)- plane bounded by the straight line segment \(\Gamma_ 0\) at \(x_ 2=0\), by the straight line segment \(\Gamma_ L\) at \(x_ 2=L\) (which may, in limiting cases, contract to a point), and by curves \((C^-):x_ 1=x^- _ 1(x_ 2)\), \((C^+):x_ 1=x^+_ 1(x_ 2)\), \(x^-_ 1(x_ 2)\leq x^+_ 1(x_ 2)
Flavin, J. N., Knops, R. J.
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On the traction problem for linear elastostatics in exterior domains
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1984SynopsisIn this note, we study the well-posedness of the exterior traction value problem for linear anisotropic non-homogeneous elastostatics. We prove existence and continuous dependence upon the data. In particular, in the isotropic homogeneous case, provided the body force is “simple”, we show that solutions tend to zero uniformly at large spatial ...
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