对数应变张量的近似计算公式

Approximate Formulae of the Logarithmic Strain Tensor

基于泰勒展开给出对数应变张量的级数表示,利用选取不同的项数和不同的展开点,得到对数应变张量的误差最小近似表达式。结合简单实例,对近似计算结果的精度和计算时间与精确解进行比较。结果表明,获得的对数应变张量近似表达式不但简单,而且计算时间短、精度高、适用范围也相当广泛。

Based on the Taylor expansion, the expressions of the logarithmic strain tensor in series forms are given. Through choosing different expending points and different number of terms, some approximate formulae are obtained. By using of some examples, the accuracy and calculating time of the results by the approximate formulae are compared with accurate solution. It is shown that the represent approximate formulae are of the simple forms, short calculating time, high accurate and widely applicability.