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In this paper, we apply the traction method that was proposed as a solution to the domain optimization problems to elliptic boundary value problems. The problems treated are those which determine the domain that minimizes a mass under constraints in specified vibration eigenvalues. Using the Lagrange multiplier method, we obtain the shape gradient functions for these domain optimization problems from the  optimality criteria. A numerical analysis technique for the multiconstraint problems is also presented. We show the successful resolution of the problems of beamlike plates clamped at both ends.", "subitem_description_type": "Abstract"}]}, "item_10_identifier_60": {"attribute_name": "URI", "attribute_value_mlt": [{"subitem_identifier_type": "HDL", "subitem_identifier_uri": "http://hdl.handle.net/2237/7245"}]}, "item_10_publisher_32": {"attribute_name": "\u51fa\u7248\u8005", "attribute_value_mlt": [{"subitem_publisher": "\u65e5\u672c\u6a5f\u68b0\u5b66\u4f1a"}]}, "item_10_rights_12": {"attribute_name": "\u6a29\u5229", "attribute_value_mlt": [{"subitem_rights": "\u65e5\u672c\u6a5f\u68b0\u5b66\u4f1a"}]}, "item_10_select_15": {"attribute_name": "\u8457\u8005\u7248\u30d5\u30e9\u30b0", "attribute_value_mlt": [{"subitem_select_item": "publisher"}]}, "item_10_source_id_7": {"attribute_name": "ISSN", "attribute_value_mlt": [{"subitem_source_identifier": "0387-5024", "subitem_source_identifier_type": "ISSN"}]}, "item_10_text_14": {"attribute_name": "\u30d5\u30a9\u30fc\u30de\u30c3\u30c8", 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