Reliability of composites in a random stress state

A general problem of reliability evaluation of an anisotropic material in a random 2-D or 3-D stress state is considered. Here, reliability is defined as a probability of the material non-failure. Strength characteristics of the material are also considered as random ones and determined by the respective mean values and all possible correlations. In contrast with the existing numerical or approximate methods, a simple analytical approach is offered for evaluating the main statistical characteristics of the reliability. A fundamental idea of the approach consists of analysis of the material's failure envelope in the form of a random linear function of certain non-linear combinations (products) of applied random stresses, instead of the traditional consideration of the envelope as a random non-linear function of the stresses. Thus, the approach allows one to take into consideration all possible kinds of failure envelopes in the simplest analytical form. Analytical expressions regarding calculation of necessary statistical characteristics are presented. Numerical examples of reliability evaluation are considered for unidirectional and laminated composites.

[1]  Stephen W. Tsai,et al.  A General Theory of Strength for Anisotropic Materials , 1971 .

[2]  A. M. Hasofer,et al.  Exact and Invariant Second-Moment Code Format , 1974 .

[3]  Yoshisada Murotsu,et al.  Reliability of unidirectional fibrous composites , 1990 .

[4]  Walter Ledermann,et al.  Handbook of applicable mathematics , 1980 .

[5]  R. Rackwitz,et al.  Quadratic Limit States in Structural Reliability , 1979 .

[6]  Yoshisada Murotsu,et al.  Application of lamination parameters to reliability-based stiffness design of composites , 1993 .

[7]  K. Breitung.  Asymptotic approximations for multinormal integrals , 1984 .

[8]  M. Miki,et al.  Reliability of the strength of unidirectional fibrous composites , 1989 .

[9]  A. K. Malmeister,et al.  Geometry of theories of strength , 1966 .

[10]  T. T. Soong,et al.  Random differential equations in science and engineering , 1974 .

[11]  Yoshisada Murotsu,et al.  Optimum fiber angle of unidirectional composites for load with variations , 1992 .

[12]  J. N. Reddy,et al.  Probabilistic nonlinear finite element analysis of composite structures , 1993 .

[13]  Hidetoshi Nakayasu,et al.  Reliability-Oriented Materials Design of Composite Materials , 1990 .

[14]  Yoshisada Murotsu,et al.  Optimum Fiber Orientation Angle of Multiaxially Laminated Composites Based on Reliability. , 1993 .

[15]  Yih‐Tsuen Wu,et al.  New Algorithm for Structural Reliability Estimation , 1987 .

[16]  A. Skudra.  Structural analysis of composite beam systems , 1991 .

[17]  R. Byron Pipes,et al.  Statistics of fracture of composite materials under multiaxial loading , 1984 .

[18]  C. C. Chamis.  Structural design and analysis , 1975 .

[19]  Mark R. Gurvich,et al.  Probabilistic strength analysis of four-directional laminated composites , 1996 .

[20]  R. C. Wetherhold.  The Effect of Stress Concentration on the Reliability of Composite Materials , 1985 .

[21]  Robert C. Wetherhold,et al.  Probability methods for the fracture of composite materials , 1994 .

[22]  Z. Hashin,et al.  A Fatigue Failure Criterion for Fiber Reinforced Materials , 1973 .

[23]  Chih-Chen Chang,et al.  Reliability of uncertain flexible laminated skewed plates under random compressions , 1992 .

[24]  R. Rackwitz,et al.  New light on first- and second-order reliability methods , 1987 .

[25]  B. N. Cassenti,et al.  Probabilistic Static Failure of Composite Material. , 1984 .

[26]  I. Elishakoff,et al.  Reliability of laminated plates via the first-order second-moment method , 1990 .

[27]  R. C. Wetherhold.  Reliability Calculations for Strength of a Fibrous Composite Under Multiaxial Loading , 1981 .

[28]  C. T. Sun,et al.  Strength Distribution of a Unidirectional Fiber Composite , 1978 .

[29]  R. Rackwitz,et al.  Structural reliability under combined random load sequences , 1978 .

[30]  M. Miki,et al.  Reliability Concept Applied to Optimum Configuration of Fibrous Composites , 1989 .

[31]  Radial vibrations of a regularly laminated hollow sphere , 1983 .